ANISOTROPIC NONLINEAR DIFFUSION WITH ABSORPTION: EXISTENCE AND EXTINCTION
The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constituti...
Saved in:
| Published in | International Journal of Mathematics and Mathematical Sciences Vol. 1996; no. 3; pp. 427 - 434 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Hindawi Limiteds
1996
Hindawi Limited |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions φ_(ij) and f which ensure the existence of a time t_0＞0 for which u vanishes for all t≥t_0. |
|---|---|
| AbstractList | The authors prove that the nonlinear parabolic partial differential equation ut=i,j=1n2xixjij(u)f(u) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions ij and f which ensure the existence of a time t0 > 0 for which u vanishes for all tt0. The authors prove that the nonlinear parabolic partial differential equation ∂u∂t=∑i,j=1n∂2∂xi∂xjφij(u)−f(u) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions φij and f which ensure the existence of a time t0>0 for which u vanishes for all t≥t0. The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions φ_(ij) and f which ensure the existence of a time t_0＞0 for which u vanishes for all t≥t_0. The authors prove that the nonlinear parabolic partial differential equation urn:x-wiley:01611712:media:ijmm347450:ijmm347450-math-0001 with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u . They also give necessary and sufficient conditions on the constitutive functions φ i j and f which ensure the existence of a time t 0 > 0 for which u vanishes for all t ≥ t 0 . |
| Author | ALAN V. LAIR MARK E. OXLEY |
| Author_xml | – sequence: 1 givenname: Alan V. surname: Lair fullname: Lair, Alan V. – sequence: 2 givenname: Mark E. surname: Oxley fullname: Oxley, Mark E. |
| BookMark | eNplUU1r20AQXUIKcdL-gN506k3tzGo_e1MVOVkwkrEU2tuyklZFxrHSlX3ov48Ul0LpYRjevDdvYN4tuT6OR0_IR4TPiJx_qQAFokSqBQAIhCuyQqFkDIzya7Ja6Hjhb8jtNO0BUFHKV8SkhanKelduTRYVZbExRZ7uonuzXj9Vpiyi76Z-jNJvVbnb1jP-GuU_TFXnRZZHaXE_o9oU2cK8J-96d5j8hz_9jjyt8zp7jDflg8nSTewSISFmXDUKJADvGAPtJThsOHRcuUZQp0G3su84Ni12QlHBsBeSotedY8InLrkj5uLbjW5vX8Lw7MJvO7rBvg3G8NO6cBrag7dt0gClsmt6RMY8OnA9102jBW0FKD57fbp4vYTx19lPJ_s8TK0_HNzRj-fJUsUSRVHPQrwI2zBOU_D938MIdgnA_hfAvLO57LghDKfB7sdzOM6fsVu6aIGyOQWLWguk9m1EgQJQ-S9gSyUseQX-MYWy |
| CitedBy_id | crossref_primary_10_1007_s40840_014_0028_6 crossref_primary_10_1109_4233_897062 crossref_primary_10_4236_am_2015_65071 crossref_primary_10_1016_j_na_2005_05_037 |
| ContentType | Journal Article |
| DBID | 188 AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D DOA |
| DOI | 10.1155/S0161171296000610 |
| DatabaseName | Airiti Library CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Directory of Open Access Journals |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1687-0425 |
| EndPage | 434 |
| ExternalDocumentID | oai_doaj_org_article_c3b0227dbf1144e1a0af59bb962c6085 10_1155_S0161171296000610 P20161024001_199612_201612020027_201612020027_427_434 |
| GroupedDBID | -~9 -~X 188 24P 29J 2UF 2WC 4.4 5GY 5VS AAFWJ AAJEY ABCQX ACGFO ACIPV ACIWK ADBBV AFPKN AI. AIAGR AINHJ ALMA_UNASSIGNED_HOLDINGS BCNDV C1A CNMHZ CS3 CVCKV EBS EJD ESX GROUPED_DOAJ H13 IAO IEA IL9 KQ8 L7B LO0 M~E OK1 P0W P2P REM RHU RHW RHX RNS TR2 TWZ UNMZH UPT UZ4 VH1 WH7 3V. 8FE 8FG 8R4 8R5 AAYXX ABDBF ABJCF ABUWG AFKRA ARAPS BENPR BGLVJ BPHCQ CCPQU CITATION CWDGH E3Z HCIFZ IPNFZ ITC K6V K7- L6V M7S NHB P62 PIMPY PQQKQ PROAC PTHSS Q2X RIG TUS ~8M 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-a3670-458b807005d4409e70a1b50d58ab62a909c7fd51bc1d682641f6721e9da46e3a3 |
| IEDL.DBID | DOA |
| ISSN | 0161-1712 |
| IngestDate | Mon Nov 04 19:59:25 EST 2024 Fri Aug 16 21:08:01 EDT 2024 Fri Dec 06 09:38:18 EST 2024 Tue Oct 01 22:50:55 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Anisotropic nonlinear diffusion finite extinction time generalized solution |
| Language | English |
| License | http://creativecommons.org/licenses/by/3.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a3670-458b807005d4409e70a1b50d58ab62a909c7fd51bc1d682641f6721e9da46e3a3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| OpenAccessLink | https://doaj.org/article/c3b0227dbf1144e1a0af59bb962c6085 |
| PQID | 28438219 |
| PQPubID | 23500 |
| PageCount | 8 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_c3b0227dbf1144e1a0af59bb962c6085 proquest_miscellaneous_28438219 crossref_primary_10_1155_S0161171296000610 airiti_journals_P20161024001_199612_201612020027_201612020027_427_434 |
| PublicationCentury | 1900 |
| PublicationDate | 1996-00-00 |
| PublicationDateYYYYMMDD | 1996-01-01 |
| PublicationDate_xml | – year: 1996 text: 1996-00-00 |
| PublicationDecade | 1990 |
| PublicationTitle | International Journal of Mathematics and Mathematical Sciences |
| PublicationYear | 1996 |
| Publisher | Hindawi Limiteds Hindawi Limited |
| Publisher_xml | – name: Hindawi Limiteds – name: Hindawi Limited |
| SSID | ssj0018225 |
| Score | 1.4459164 |
| Snippet | The authors prove that the nonlinear parabolic partial differential equation (The equation is abbreviated) with homogeneous Dirichlet boundary conditions and a... The authors prove that the nonlinear parabolic partial differential equation urn:x-wiley:01611712:media:ijmm347450:ijmm347450-math-0001 with homogeneous... The authors prove that the nonlinear parabolic partial differential equation ut=i,j=1n2xixjij(u)f(u) with homogeneous Dirichlet boundary conditions and a... The authors prove that the nonlinear parabolic partial differential equation ∂u∂t=∑i,j=1n∂2∂xi∂xjφij(u)−f(u) with homogeneous Dirichlet boundary conditions and... |
| SourceID | doaj proquest crossref airiti |
| SourceType | Open Website Aggregation Database Publisher |
| StartPage | 427 |
| SubjectTerms | Anisotropic nonlinear diffusion finite extinction time generalized solution |
| Title | ANISOTROPIC NONLINEAR DIFFUSION WITH ABSORPTION: EXISTENCE AND EXTINCTION |
| URI | https://www.airitilibrary.com/Article/Detail/P20161024001-199612-201612020027-201612020027-427-434 https://search.proquest.com/docview/28438219 https://doaj.org/article/c3b0227dbf1144e1a0af59bb962c6085 |
| Volume | 1996 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFA8iHvQgfuL87MGTUEzaJE28qWxMRVFU2C0kTQq7dLJu_7_vpZ04dvDioYU8CgkvL--7vxByqXOpfKh4GoQNKec0T21VYg3eOy1cjjKN3RYvcvjJH0di9OuqL-wJa-GBW8Zdl7lDlDvvKvDceWCW2kpo57TMSgn-QtS-NFsEU139AMxe27woWcoKlnX1TDCe1-9IRBr47mjAQRlv2DEiCC2Zpojgv6Kgo9UZ7JDtzl1Mbttl7pK1UO-RrecfrNVmnzzc1uNmMptOvsZlUrfIF3aa4M0nc0yFJZhqTaxrJtOoHm4SRL-MrnJiaw-j2biOfzcckM9B_-N-mHYXJKQWcddSLpRTcGap8MBlHQpqmRPUC2WdzKymuiwqL5grmZcQR3BWSYj4gvaWy5Db_JCsw7rCEUm49ooVTusy82DXChXPsqtCATNYRXuk3zLJdDLemNcMOYkYaZQZbGZmmYmkjGLnR7E84PjkvEeuFjw2Xy2eholxiBBmZWd65A534edDhMKOBBAQ0wmI-UtAeuRisYcGjg7WQ2wdJvPGgGXOFWjs4_-Y5oRstg3dmJ05Jeuz6Tycgb8yc-dRNOH99Ka-AQym3xw |
| link.rule.ids | 314,780,784,864,2102,4024,27923,27924,27925 |
| linkProvider | Directory of Open Access Journals |
| 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=ANISOTROPIC+NONLINEAR+DIFFUSION+WITH+ABSORPTION%3A+EXISTENCE+AND+EXTINCTION&rft.jtitle=International+Journal+of+Mathematics+and+Mathematical+Sciences&rft.au=ALAN+V.+LAIR&rft.au=MARK+E.+OXLEY&rft.date=1996&rft.pub=Hindawi+Limiteds&rft.issn=0161-1712&rft.volume=1996&rft.spage=427&rft.epage=434&rft_id=info:doi/10.1155%2FS0161171296000610&rft.externalDocID=P20161024001_199612_201612020027_201612020027_427_434 |
| thumbnail_m | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.airitilibrary.com%2Fjnltitledo%2FP20161024001-c.jpg |