Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges
We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The...
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 191; no. 2; pp. 254 - 279 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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13.05.2013
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| Abstract | We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as
ε
→ 0. Bibliography: 26 titles. Illustrations: 2 figures. |
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| AbstractList | We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ζ-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as ζ → 0. Bibliography:26 titles. Illustrations: 2 figures. We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed thin disks. The thin disks are divided into two levels depending on their geometric structure and boundary conditions on their surfaces. The first-level thin disks have variable thickness vanishing at their edges. Hence some coefficients of the corresponding homogenized problem degenerate and its solution has a singular behavior near the boundary. We extract three qualitatively different cases of the asymptotic behavior of the solution as ε → 0. Bibliography: 26 titles. Illustrations: 2 figures. |
| Audience | Academic |
| Author | Mel’nik, T. A. Sadovyi, D. Yu |
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| Keywords | Thin Disk Integral Identity Weak Derivative Weak Solution Unique Weak Solution |
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| References | Nazarov (CR20) 2011; 52 Mel’nik, Nazarov (CR5) 2001; 12 De Maio, Mel’nyk (CR24) 2005; 41 Cardone, Durante, Nazarov (CR18) 2010; 42 Nazarov, Taskinen (CR21) 2007; 142 Vishik (CR17) 1954; 35 De Maio, Mel’nyk (CR26) 2005; 28 Arrieta, Carvalho, Pereira, Silva (CR10) 2011; 74 Grisvard (CR25) 1985 Mel’nyk (CR2) 1999; 18 Chechkin, Mel’nyk (CR14) 2012; 91 Blanchard, Gaudiello, Griso (CR12) 2007; 88 Blanchard, Gaudiello, Mel’nyk (CR13) 2008; 39 Blanchard, Gaudiello, Griso (CR11) 2007; 88 Ladyzhenskaya (CR23) 1985 Lenczner (CR7) 2007; 90 Mel’nik, Nazarov (CR4) 1997; 85 Nazarov, Taskinen (CR22) 2011; 45 Fleury, Sánchez-Palencia (CR1) 1986; 110 Mel’nik, Nazarov (CR3) 1994; 48 Amirat, Chechkin, Gadyl’shin (CR9) 2010; 11 Nazarov (CR19) 2008); 49 Lyshevshi (CR8) 2002 Mel’nyk, Nakvasiuk, Wendland (CR15) 2011; 34 Nazarov (CR6) 1996; 80 Mel’nik, Sadovyi (CR16) 2010; 165 TA Mel’nik (1315_CR4) 1997; 85 TA Mel’nik (1315_CR16) 2010; 165 SA Nazarov (1315_CR6) 1996; 80 D Blanchard (1315_CR12) 2007; 88 JM Arrieta (1315_CR10) 2011; 74 D Blanchard (1315_CR13) 2008; 39 Y Amirat (1315_CR9) 2010; 11 M Lenczner (1315_CR7) 2007; 90 F Fleury (1315_CR1) 1986; 110 TA Mel’nyk (1315_CR2) 1999; 18 TA Mel’nik (1315_CR5) 2001; 12 D Blanchard (1315_CR11) 2007; 88 U Maio De (1315_CR26) 2005; 28 MI Vishik (1315_CR17) 1954; 35 GA Chechkin (1315_CR14) 2012; 91 P Grisvard (1315_CR25) 1985 SA Nazarov (1315_CR19) 2008); 49 TA Mel’nyk (1315_CR15) 2011; 34 U Maio De (1315_CR24) 2005; 41 G Cardone (1315_CR18) 2010; 42 SE Lyshevshi (1315_CR8) 2002 SA Nazarov (1315_CR22) 2011; 45 SA Nazarov (1315_CR21) 2007; 142 TA Mel’nik (1315_CR3) 1994; 48 OA Ladyzhenskaya (1315_CR23) 1985 SA Nazarov (1315_CR20) 2011; 52 |
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Sci. doi: 10.1002/mma.1395 contributor: fullname: TA Mel’nyk – volume: 142 start-page: 2630 issue: 6 year: 2007 ident: 1315_CR21 publication-title: J. Math. Sci., New York doi: 10.1007/s10958-007-0151-0 contributor: fullname: SA Nazarov – volume: 18 start-page: 953 issue: 4 year: 1999 ident: 1315_CR2 publication-title: Z. Anal. Anw. doi: 10.4171/ZAA/923 contributor: fullname: TA Mel’nyk – volume: 11 start-page: 4492 issue: 6 year: 2010 ident: 1315_CR9 publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2008.11.023 contributor: fullname: Y Amirat |
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| Snippet | We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ε-periodically stringed... We consider a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with ζ-periodically stringed... |
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| Title | Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges |
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