Error estimates of effective boundary conditions for the heat equation with optimally aligned coatings
We are interested in the validity of effective boundary conditions for a heat equation on a coated body as the thickness of the coating shrinks to zero. The coating is optimally aligned in the sense that the normal vector in the coating is an eigenvector of the thermal tensor. If the heat equation s...
Saved in:
| Published in | Journal of mathematical analysis and applications Vol. 543; no. 1; p. 128972 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.03.2025
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We are interested in the validity of effective boundary conditions for a heat equation on a coated body as the thickness of the coating shrinks to zero. The coating is optimally aligned in the sense that the normal vector in the coating is an eigenvector of the thermal tensor. If the heat equation satisfies Neumann boundary condition on the outer boundary of the coating, Chen et al. (Arch. Ration. Mech. Anal. 206 (2012) 911-951) derived the complete list of effective boundary conditions satisfied by the limiting model. In this paper we provide explicit error estimates between the full model and the effective model. Moreover, our error estimates are independent of time, which shows that the maximal time interval in which the effective boundary conditions remain valid are infinite. The proof is based on H2 estimates for solutions of the full model, characterization of large time behaviors for solutions of the effective model, and interaction estimates between the two models. |
|---|---|
| AbstractList | We are interested in the validity of effective boundary conditions for a heat equation on a coated body as the thickness of the coating shrinks to zero. The coating is optimally aligned in the sense that the normal vector in the coating is an eigenvector of the thermal tensor. If the heat equation satisfies Neumann boundary condition on the outer boundary of the coating, Chen et al. (Arch. Ration. Mech. Anal. 206 (2012) 911-951) derived the complete list of effective boundary conditions satisfied by the limiting model. In this paper we provide explicit error estimates between the full model and the effective model. Moreover, our error estimates are independent of time, which shows that the maximal time interval in which the effective boundary conditions remain valid are infinite. The proof is based on H2 estimates for solutions of the full model, characterization of large time behaviors for solutions of the effective model, and interaction estimates between the two models. |
| ArticleNumber | 128972 |
| Author | Zhou, Zhitong Meng, Lixin |
| Author_xml | – sequence: 1 givenname: Lixin surname: Meng fullname: Meng, Lixin email: menglx790@nenu.edu.cn organization: School of Statistics, Jilin University of Finance and Economics, Changchun, 130117, China – sequence: 2 givenname: Zhitong surname: Zhou fullname: Zhou, Zhitong email: zhouzt938@nenu.edu.cn organization: The High School Affiliated to Liaoning Normal University, Dalian, Liaoning, 116023, China |
| BookMark | eNp9kMtOAyEYhVnUxLb6Aq54gRmBzjCQuDFNvSRN3GjijlDmp2UyhQq0pm_vjHXt6uS_nJOTb4YmPnhA6I6SkhLK77uy22tdMsKqkjIhGzZBU0IYK1jVfF6jWUodIZTWDZ0iu4oxRAwpu73OkHCwGKwFk90J8CYcfavjGZvgW5dd8Anb4T3vAO9AZwxfRz2u8bfLOxwOY0rfn7Hu3dZDO_iGs9-mG3RldZ_g9k_n6ONp9b58KdZvz6_Lx3VhqKC5kJrUfEHMwrTQyEpyKaCuBefSVIab2sjfSQjGJG9IM-hGcGIqq0WtOVvMEbvkmhhSimDVIQ6V4llRokY6qlMjHTXSURc6g-nhYoKh2clBVMk48AZaFwcQqg3uP_sPD4RyoA |
| Cites_doi | 10.1007/BF01442194 10.3934/cpaa.2009.8.1251 10.3934/dcds.2016.36.1415 10.1016/j.matpur.2005.10.013 10.1142/S0218202511005283 10.3934/nhm.2011.6.1 10.1016/j.matpur.2006.08.003 10.1090/S0002-9939-08-09766-9 10.1137/040621181 10.1007/BF00283252 10.1016/j.jde.2021.09.015 10.4208/cmr.2020-0012 10.1016/s0294-1449(16)30380-8 10.1216/RMJ-2012-42-3-937 10.1007/BF01796546 10.1007/s00526-015-0882-6 10.1016/j.jde.2020.09.011 10.1007/s00205-012-0547-y 10.1016/j.jde.2021.04.011 10.1016/j.jde.2014.07.004 10.1088/1361-6544/aa82ee 10.3934/cpaa.2017071 10.1007/s000330300008 10.3934/dcds.2009.25.1061 10.1063/5.0083001 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier Inc. |
| Copyright_xml | – notice: 2024 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.jmaa.2024.128972 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| ExternalDocumentID | 10_1016_j_jmaa_2024_128972 S0022247X24008941 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 4.4 457 4G. 5GY 71M 85S 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AASFE AAXKI AAXUO ABAOU ABJNI ABMAC ABVKL ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AFJKZ AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DM4 EBS EFBJH EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM MCRUF MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW T5K TN5 TWZ UPT WH7 XPP YQT ZMT ZU3 ~G- 1~5 29L 5VS 6I. 6TJ 7-5 AAQXK AAYXX ABDPE ABEFU ABFNM ABXDB ACRPL ADFGL ADIYS ADMUD ADNMO ADVLN AEXQZ AFFNX AGHFR AI. ASPBG AVWKF AZFZN CAG CITATION COF EJD FGOYB G-2 HZ~ H~9 LG5 M25 M41 MVM NCXOZ OHT R2- SSZ VH1 VOH WUQ XOL YYP ZCG |
| ID | FETCH-LOGICAL-c181t-9a05630c3cde7949698e558669c4c6c5c955866882296707822b860c4fa85a623 |
| IEDL.DBID | AIKHN |
| ISSN | 0022-247X |
| IngestDate | Fri Dec 06 07:22:22 EST 2024 Sat Nov 16 15:59:34 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Eigenvalue Error estimates Heat equation Effective boundary conditions Optimally aligned coatings |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c181t-9a05630c3cde7949698e558669c4c6c5c955866882296707822b860c4fa85a623 |
| ParticipantIDs | crossref_primary_10_1016_j_jmaa_2024_128972 elsevier_sciencedirect_doi_10_1016_j_jmaa_2024_128972 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-01 2025-03-00 |
| PublicationDateYYYYMMDD | 2025-03-01 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of mathematical analysis and applications |
| PublicationYear | 2025 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Li, Wang, Zhang, Zhang (br0240) 2012; 42 Acerbi, Buttazzo (br0010) 1986; 3 Mabrouk, Samadi (br0260) 2003; 54 Carslaw, Jaeger (br0050) 1959 Li, Zhang (br0250) 2011; 21 Li, Su, Wang, Wang (br0230) 2021; 289 Li, Li (br0160) 2022; 63 Gómez, Nazarov, Pérez-Martínez (br0130) 2021; 270 Mercaldo, Mossino, Prignet (br0270) 2008; 56 Gilbarg, Trudinger (br0090) 1998 Buttazzo, Kohn (br0030) 1987; 16 Gómez, Nazarov, Pérez (br0120) 2011; 6 Friedman (br0080) 1980; 73 Sanchez-Palencia (br0290) 1974; 53 Li, Wang, Wu (br0200) 2014; 257 Li (br0140) 2016; 36 Li, Wang (br0180) 2017; 30 Li, Wang (br0190) 2020; 36 Li (br0210) 2009; 8 Wang (br0300) 2016; 46 Chen, Pond, Wang (br0060) 2012; 206 Li, Li, Wang (br0170) 2021; 303 Gómez, Lobo, Nazarov, Pérez (br0110) 2006; 86 Zhang, Rosencrans, Wang, Zhang (br0310) 2009; 25 Capitanelli, Vivaldi (br0040) 2015; 54 Li, Li (br0150) 2017; 16 De Giorgi, Franzoni (br0070) 1975; 58 Gómez, Lobo, Nazarov, Pérez (br0100) 2006; 85 Rosencrans, Wang (br0280) 2006; 66 Brezis, Caffarelli, Friedman (br0020) 1980; 123 Li, Rosencrans, Wang, Zhang (br0220) 2009; 137 Li (10.1016/j.jmaa.2024.128972_br0140) 2016; 36 Wang (10.1016/j.jmaa.2024.128972_br0300) 2016; 46 Carslaw (10.1016/j.jmaa.2024.128972_br0050) 1959 Brezis (10.1016/j.jmaa.2024.128972_br0020) 1980; 123 Chen (10.1016/j.jmaa.2024.128972_br0060) 2012; 206 Mercaldo (10.1016/j.jmaa.2024.128972_br0270) 2008; 56 Gilbarg (10.1016/j.jmaa.2024.128972_br0090) 1998 Li (10.1016/j.jmaa.2024.128972_br0200) 2014; 257 Li (10.1016/j.jmaa.2024.128972_br0160) 2022; 63 Li (10.1016/j.jmaa.2024.128972_br0190) 2020; 36 Gómez (10.1016/j.jmaa.2024.128972_br0110) 2006; 86 Rosencrans (10.1016/j.jmaa.2024.128972_br0280) 2006; 66 Capitanelli (10.1016/j.jmaa.2024.128972_br0040) 2015; 54 De Giorgi (10.1016/j.jmaa.2024.128972_br0070) 1975; 58 Li (10.1016/j.jmaa.2024.128972_br0150) 2017; 16 Li (10.1016/j.jmaa.2024.128972_br0180) 2017; 30 Li (10.1016/j.jmaa.2024.128972_br0170) 2021; 303 Li (10.1016/j.jmaa.2024.128972_br0210) 2009; 8 Gómez (10.1016/j.jmaa.2024.128972_br0120) 2011; 6 Buttazzo (10.1016/j.jmaa.2024.128972_br0030) 1987; 16 Gómez (10.1016/j.jmaa.2024.128972_br0130) 2021; 270 Li (10.1016/j.jmaa.2024.128972_br0220) 2009; 137 Sanchez-Palencia (10.1016/j.jmaa.2024.128972_br0290) 1974; 53 Zhang (10.1016/j.jmaa.2024.128972_br0310) 2009; 25 Gómez (10.1016/j.jmaa.2024.128972_br0100) 2006; 85 Acerbi (10.1016/j.jmaa.2024.128972_br0010) 1986; 3 Li (10.1016/j.jmaa.2024.128972_br0240) 2012; 42 Li (10.1016/j.jmaa.2024.128972_br0250) 2011; 21 Friedman (10.1016/j.jmaa.2024.128972_br0080) 1980; 73 Mabrouk (10.1016/j.jmaa.2024.128972_br0260) 2003; 54 Li (10.1016/j.jmaa.2024.128972_br0230) 2021; 289 |
| References_xml | – volume: 42 start-page: 937 year: 2012 end-page: 958 ident: br0240 article-title: Asymptotic behavior of Robin problem for heat equation on a coated body publication-title: Rocky Mt. J. Math. contributor: fullname: Zhang – volume: 36 start-page: 272 year: 2020 end-page: 295 ident: br0190 article-title: Effective boundary conditions for the heat equation with interior inclusion publication-title: Commun. Math. Res. contributor: fullname: Wang – volume: 56 start-page: 37 year: 2008 end-page: 59 ident: br0270 article-title: Nonlinear reinforcement problems with right-hand side in publication-title: Asymptot. Anal. contributor: fullname: Prignet – volume: 16 start-page: 247 year: 1987 end-page: 261 ident: br0030 article-title: Reinforcement by a thin layer with oscillating thickness publication-title: Appl. Math. Optim. contributor: fullname: Kohn – volume: 137 start-page: 1711 year: 2009 end-page: 1721 ident: br0220 article-title: Asymptotic analysis of a Dirichlet problem for the heat equation on a coated body publication-title: Proc. Am. Math. Soc. contributor: fullname: Zhang – volume: 3 start-page: 273 year: 1986 end-page: 284 ident: br0010 article-title: Reinforcement problems in the calculus of variations publication-title: Ann. Inst. Henri Poincaré, Anal. Non Linéaire contributor: fullname: Buttazzo – volume: 54 start-page: 349 year: 2003 end-page: 375 ident: br0260 article-title: Linear and semi-linear reinforcement problems by thin layers publication-title: Z. Angew. Math. Phys. contributor: fullname: Samadi – volume: 58 start-page: 842 year: 1975 end-page: 850 ident: br0070 article-title: Su un tipo di convergenza variazionale (Italian) publication-title: Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat. contributor: fullname: Franzoni – volume: 36 start-page: 1415 year: 2016 end-page: 1430 ident: br0140 article-title: Effective boundary conditions of the heat equation on a body coated by functionally graded material publication-title: Discrete Contin. Dyn. Syst. contributor: fullname: Li – volume: 54 start-page: 2751 year: 2015 end-page: 2783 ident: br0040 article-title: Reinforcement problems for variational inequalities on fractal sets publication-title: Calc. Var. Partial Differ. Equ. contributor: fullname: Vivaldi – volume: 21 start-page: 1153 year: 2011 end-page: 1192 ident: br0250 article-title: Reinforcement of the Poisson equation by a thin layer publication-title: Math. Models Methods Appl. Sci. contributor: fullname: Zhang – year: 1959 ident: br0050 article-title: Conduction of Heat in Solids contributor: fullname: Jaeger – volume: 25 start-page: 1061 year: 2009 end-page: 1079 ident: br0310 article-title: Estimating thermal insulating ability of anisotropic coatings via Robin eigenvalues and eigenfunctions publication-title: Discrete Contin. Dyn. Syst. contributor: fullname: Zhang – volume: 123 start-page: 219 year: 1980 end-page: 246 ident: br0020 article-title: Reinforcement problems for elliptic equations and variational inequalities publication-title: Ann. Mat. Pura Appl. contributor: fullname: Friedman – volume: 16 start-page: 1493 year: 2017 end-page: 1516 ident: br0150 article-title: Asymptotic behavior of Dirichlet eigenvalues on a body coated by functionally graded material publication-title: Commun. Pure Appl. Anal. contributor: fullname: Li – volume: 8 start-page: 1251 year: 2009 end-page: 1267 ident: br0210 article-title: Asymptotic behavior of solutions to elliptic equations in a coated body publication-title: Commun. Pure Appl. Anal. contributor: fullname: Li – volume: 73 start-page: 1 year: 1980 end-page: 17 ident: br0080 article-title: Reinforcement of the principal eigenvalue of an elliptic operator publication-title: Arch. Ration. Mech. Anal. contributor: fullname: Friedman – volume: 303 start-page: 1 year: 2021 end-page: 41 ident: br0170 article-title: Error estimates and lifespan of effective boundary conditions for 2-dimensional optimally aligned coatings publication-title: J. Differ. Equ. contributor: fullname: Wang – volume: 85 start-page: 598 year: 2006 end-page: 632 ident: br0100 article-title: Spectral stiff problem in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues publication-title: J. Math. Pures Appl. contributor: fullname: Pérez – volume: 257 start-page: 3640 year: 2014 end-page: 3668 ident: br0200 article-title: The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body publication-title: J. Differ. Equ. contributor: fullname: Wu – volume: 206 start-page: 911 year: 2012 end-page: 951 ident: br0060 article-title: Effective boundary conditions resulting from anisotropic and optimally aligned coatings: the two dimensional case publication-title: Arch. Ration. Mech. Anal. contributor: fullname: Wang – volume: 6 start-page: 1 year: 2011 end-page: 35 ident: br0120 article-title: Spectral stiff problem in domains surrounded by thin stiff and heavy bands: local effects for eigenfunctions publication-title: Netw. Heterog. Media contributor: fullname: Pérez – volume: 270 start-page: 1160 year: 2021 end-page: 1195 ident: br0130 article-title: Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands publication-title: J. Differ. Equ. contributor: fullname: Pérez-Martínez – volume: 46 start-page: 709 year: 2016 end-page: 724 ident: br0300 article-title: Effective boundary conditions of diffusion equations on domains containing thin layers publication-title: Sci. Sin., Math. contributor: fullname: Wang – volume: 63 year: 2022 ident: br0160 article-title: Lifespan of effective boundary conditions for the heat equation publication-title: J. Math. Phys. contributor: fullname: Li – volume: 66 start-page: 1895 year: 2006 end-page: 1916 ident: br0280 article-title: Suppression of the Dirichlet eigenvalues of a coated body publication-title: SIAM J. Appl. Math. contributor: fullname: Wang – volume: 53 start-page: 251 year: 1974 end-page: 269 ident: br0290 article-title: Problèmes de perturbations liés aux phénomènes de conduction à travers des couches minces de grande résistivité publication-title: J. Math. Pures Appl. contributor: fullname: Sanchez-Palencia – year: 1998 ident: br0090 article-title: Elliptic Partial Differential Equations of Second Order publication-title: Classics in Mathematics contributor: fullname: Trudinger – volume: 289 start-page: 1 year: 2021 end-page: 34 ident: br0230 article-title: Bulk-surface coupling: derivation of two models publication-title: J. Differ. Equ. contributor: fullname: Wang – volume: 30 start-page: 3853 year: 2017 end-page: 3894 ident: br0180 article-title: Using effective boundary conditions to model fast diffusion on a road in a large field publication-title: Nonlinearity contributor: fullname: Wang – volume: 86 start-page: 369 year: 2006 end-page: 402 ident: br0110 article-title: Asymptotics for the spectrum of the Wentzell problem with a small parameter and other related stiff problems publication-title: J. Math. Pures Appl. contributor: fullname: Pérez – volume: 16 start-page: 247 year: 1987 ident: 10.1016/j.jmaa.2024.128972_br0030 article-title: Reinforcement by a thin layer with oscillating thickness publication-title: Appl. Math. Optim. doi: 10.1007/BF01442194 contributor: fullname: Buttazzo – volume: 8 start-page: 1251 year: 2009 ident: 10.1016/j.jmaa.2024.128972_br0210 article-title: Asymptotic behavior of solutions to elliptic equations in a coated body publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2009.8.1251 contributor: fullname: Li – volume: 36 start-page: 1415 year: 2016 ident: 10.1016/j.jmaa.2024.128972_br0140 article-title: Effective boundary conditions of the heat equation on a body coated by functionally graded material publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2016.36.1415 contributor: fullname: Li – year: 1959 ident: 10.1016/j.jmaa.2024.128972_br0050 contributor: fullname: Carslaw – volume: 85 start-page: 598 year: 2006 ident: 10.1016/j.jmaa.2024.128972_br0100 article-title: Spectral stiff problem in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2005.10.013 contributor: fullname: Gómez – volume: 21 start-page: 1153 year: 2011 ident: 10.1016/j.jmaa.2024.128972_br0250 article-title: Reinforcement of the Poisson equation by a thin layer publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202511005283 contributor: fullname: Li – volume: 6 start-page: 1 year: 2011 ident: 10.1016/j.jmaa.2024.128972_br0120 article-title: Spectral stiff problem in domains surrounded by thin stiff and heavy bands: local effects for eigenfunctions publication-title: Netw. Heterog. Media doi: 10.3934/nhm.2011.6.1 contributor: fullname: Gómez – volume: 86 start-page: 369 year: 2006 ident: 10.1016/j.jmaa.2024.128972_br0110 article-title: Asymptotics for the spectrum of the Wentzell problem with a small parameter and other related stiff problems publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2006.08.003 contributor: fullname: Gómez – volume: 137 start-page: 1711 year: 2009 ident: 10.1016/j.jmaa.2024.128972_br0220 article-title: Asymptotic analysis of a Dirichlet problem for the heat equation on a coated body publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-08-09766-9 contributor: fullname: Li – volume: 66 start-page: 1895 year: 2006 ident: 10.1016/j.jmaa.2024.128972_br0280 article-title: Suppression of the Dirichlet eigenvalues of a coated body publication-title: SIAM J. Appl. Math. doi: 10.1137/040621181 contributor: fullname: Rosencrans – volume: 73 start-page: 1 year: 1980 ident: 10.1016/j.jmaa.2024.128972_br0080 article-title: Reinforcement of the principal eigenvalue of an elliptic operator publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00283252 contributor: fullname: Friedman – volume: 303 start-page: 1 year: 2021 ident: 10.1016/j.jmaa.2024.128972_br0170 article-title: Error estimates and lifespan of effective boundary conditions for 2-dimensional optimally aligned coatings publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2021.09.015 contributor: fullname: Li – volume: 36 start-page: 272 year: 2020 ident: 10.1016/j.jmaa.2024.128972_br0190 article-title: Effective boundary conditions for the heat equation with interior inclusion publication-title: Commun. Math. Res. doi: 10.4208/cmr.2020-0012 contributor: fullname: Li – volume: 3 start-page: 273 year: 1986 ident: 10.1016/j.jmaa.2024.128972_br0010 article-title: Reinforcement problems in the calculus of variations publication-title: Ann. Inst. Henri Poincaré, Anal. Non Linéaire doi: 10.1016/s0294-1449(16)30380-8 contributor: fullname: Acerbi – volume: 42 start-page: 937 year: 2012 ident: 10.1016/j.jmaa.2024.128972_br0240 article-title: Asymptotic behavior of Robin problem for heat equation on a coated body publication-title: Rocky Mt. J. Math. doi: 10.1216/RMJ-2012-42-3-937 contributor: fullname: Li – volume: 123 start-page: 219 year: 1980 ident: 10.1016/j.jmaa.2024.128972_br0020 article-title: Reinforcement problems for elliptic equations and variational inequalities publication-title: Ann. Mat. Pura Appl. doi: 10.1007/BF01796546 contributor: fullname: Brezis – volume: 54 start-page: 2751 year: 2015 ident: 10.1016/j.jmaa.2024.128972_br0040 article-title: Reinforcement problems for variational inequalities on fractal sets publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s00526-015-0882-6 contributor: fullname: Capitanelli – year: 1998 ident: 10.1016/j.jmaa.2024.128972_br0090 article-title: Elliptic Partial Differential Equations of Second Order contributor: fullname: Gilbarg – volume: 270 start-page: 1160 year: 2021 ident: 10.1016/j.jmaa.2024.128972_br0130 article-title: Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2020.09.011 contributor: fullname: Gómez – volume: 46 start-page: 709 year: 2016 ident: 10.1016/j.jmaa.2024.128972_br0300 article-title: Effective boundary conditions of diffusion equations on domains containing thin layers publication-title: Sci. Sin., Math. contributor: fullname: Wang – volume: 206 start-page: 911 year: 2012 ident: 10.1016/j.jmaa.2024.128972_br0060 article-title: Effective boundary conditions resulting from anisotropic and optimally aligned coatings: the two dimensional case publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-012-0547-y contributor: fullname: Chen – volume: 289 start-page: 1 year: 2021 ident: 10.1016/j.jmaa.2024.128972_br0230 article-title: Bulk-surface coupling: derivation of two models publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2021.04.011 contributor: fullname: Li – volume: 257 start-page: 3640 year: 2014 ident: 10.1016/j.jmaa.2024.128972_br0200 article-title: The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2014.07.004 contributor: fullname: Li – volume: 53 start-page: 251 year: 1974 ident: 10.1016/j.jmaa.2024.128972_br0290 article-title: Problèmes de perturbations liés aux phénomènes de conduction à travers des couches minces de grande résistivité publication-title: J. Math. Pures Appl. contributor: fullname: Sanchez-Palencia – volume: 30 start-page: 3853 year: 2017 ident: 10.1016/j.jmaa.2024.128972_br0180 article-title: Using effective boundary conditions to model fast diffusion on a road in a large field publication-title: Nonlinearity doi: 10.1088/1361-6544/aa82ee contributor: fullname: Li – volume: 16 start-page: 1493 year: 2017 ident: 10.1016/j.jmaa.2024.128972_br0150 article-title: Asymptotic behavior of Dirichlet eigenvalues on a body coated by functionally graded material publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2017071 contributor: fullname: Li – volume: 54 start-page: 349 year: 2003 ident: 10.1016/j.jmaa.2024.128972_br0260 article-title: Linear and semi-linear reinforcement problems by thin layers publication-title: Z. Angew. Math. Phys. doi: 10.1007/s000330300008 contributor: fullname: Mabrouk – volume: 25 start-page: 1061 year: 2009 ident: 10.1016/j.jmaa.2024.128972_br0310 article-title: Estimating thermal insulating ability of anisotropic coatings via Robin eigenvalues and eigenfunctions publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2009.25.1061 contributor: fullname: Zhang – volume: 63 year: 2022 ident: 10.1016/j.jmaa.2024.128972_br0160 article-title: Lifespan of effective boundary conditions for the heat equation publication-title: J. Math. Phys. doi: 10.1063/5.0083001 contributor: fullname: Li – volume: 56 start-page: 37 year: 2008 ident: 10.1016/j.jmaa.2024.128972_br0270 article-title: Nonlinear reinforcement problems with right-hand side in L1 publication-title: Asymptot. Anal. contributor: fullname: Mercaldo – volume: 58 start-page: 842 year: 1975 ident: 10.1016/j.jmaa.2024.128972_br0070 article-title: Su un tipo di convergenza variazionale (Italian) publication-title: Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat. contributor: fullname: De Giorgi |
| SSID | ssj0011571 |
| Score | 2.4940193 |
| Snippet | We are interested in the validity of effective boundary conditions for a heat equation on a coated body as the thickness of the coating shrinks to zero. The... |
| SourceID | crossref elsevier |
| SourceType | Aggregation Database Publisher |
| StartPage | 128972 |
| SubjectTerms | Effective boundary conditions Eigenvalue Error estimates Heat equation Optimally aligned coatings |
| Title | Error estimates of effective boundary conditions for the heat equation with optimally aligned coatings |
| URI | https://dx.doi.org/10.1016/j.jmaa.2024.128972 |
| Volume | 543 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT8IwFG4QLnow_oz4Kz14M4OtW7v1SAgEJXIwErktXdcaCDAceODi327fuhFNjAdPy5a8Zvm2fe91_d5XhO6UFoRT4TuEaDNBSaV2OFeeE8kwpYlWXCaFynfEBuPgcUInNdStemFAVllyv-X0gq3LK-0SzfZqOoUeX5PbgnACKsiIQ_N6w6QjWKttdB6Gg9FuMcGjoVeZhkNA2TtjZV6zhQD7IRK0DFPzkPyen77lnP4ROiyLRdyx93OMamp5gg6edk6r61Oke3me5Ri8MhZQNuJMY6vRMDSGk2LTpHyLzaw3teIsbKpUbAbAwMJYvVurbwz_Y3G2glHm8y021fmbIWATJ0AXvT5D437vpTtwyr0THGly9sbhwgXnL-nLVJlPjjMeKUojxrgMJJNU8uIsAr93VrjmkSRirgy0iKgwNdE5qi-zpbpAmHCifTfVLljBceEJrV1fMuL6ylM04U10XyEWr6xFRlxpx2Yx4BsDvrHFt4loBWr840HHhsP_iLv8Z9wV2iewZW8hG7tG9U3-oW5MHbFJbtFe69O7Ld8WOA6fX4dfAcPJSw |
| link.rule.ids | 314,780,784,4502,24116,27924,27925,45585,45679 |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT8IwGG0IHtSD8WfEnz14M4PRbWU9GgJBBU6QcFu6rjUQYDjwwMW_3e9bN6KJ8eBxy9osb9373pb3vRLyoI1kIpCew5iBD5REGUcI3XRC1UqC2Gih4tzlO-S9sf8yCSYV0i57YdBWWXC_5fScrYszjQLNxmo6xR5fqG1-a4IuyFBg8_qeH4D6hUVd_9z5PDBMpllGhuPlReeMNXnNFhLDh5hfB54WLfZ7dfpWcbrH5KiQivTJ3s0JqejlKTkc7HJW12fEdLIszSgmZSxQNNLUUOvQABKjcb5lUral8M2bWGsWBY1KYQKKHEz1uw36pvg3lqYrnGU-31LQ5m9AvzBOoit6fU7G3c6o3XOKnRMcBRV74wjpYu6X8lSi4YUTXIQaoOFcKF9xFSiRH4WY9s7zzDwWh9xVvpFhIEERXZDqMl3qS0KZYMZzE-NiEJyQTWmM6ynOXE83dRCLGnksEYtWNiAjKp1jswjxjRDfyOJbI0EJavTjMUfA4H-Mu_rnuHuy3xsN-lH_efh6TQ4Ybt6bG8huSHWTfehbUBSb-C5fMV-HFMiB |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Error+estimates+of+effective+boundary+conditions+for+the+heat+equation+with+optimally+aligned+coatings&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Meng%2C+Lixin&rft.au=Zhou%2C+Zhitong&rft.date=2025-03-01&rft.issn=0022-247X&rft.volume=543&rft.issue=1&rft.spage=128972&rft_id=info:doi/10.1016%2Fj.jmaa.2024.128972&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jmaa_2024_128972 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon |