A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions
Our main interest in this article is the study of homogenized limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with periodically place particles. We focus on the case of particles (or holes) of critical diameter with respect to th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2019-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/77/abstr.html |
| _version_ | 1828518126517485568 |
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| author | Jesus Ildefonso Diaz David Gomez-Castro Tatiana A. Shaposhnikova Maria N. Zubova |
| author_facet | Jesus Ildefonso Diaz David Gomez-Castro Tatiana A. Shaposhnikova Maria N. Zubova |
| author_sort | Jesus Ildefonso Diaz |
| collection | DOAJ |
| description | Our main interest in this article is the study of homogenized limit of a
parabolic equation with a nonlinear dynamic boundary condition of the
micro-scale model set on a domain with periodically place particles.
We focus on the case of particles (or holes) of critical diameter with respect
to the period of the structure.
Our main result proves the weak convergence of the sequence of solutions of
the original problem to the solution of a reaction-diffusion parabolic problem
containing a "strange term".
The novelty of our result is that this term is a nonlocal memory solving an ODE.
We prove that the resulting system satisfies a comparison principle. |
| first_indexed | 2024-12-11T18:50:55Z |
| format | Article |
| id | doaj.art-cfd76f7a52cf417ea4f98829c6674df2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T18:50:55Z |
| publishDate | 2019-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-cfd76f7a52cf417ea4f98829c6674df22022-12-22T00:54:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-06-01201977,113A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditionsJesus Ildefonso Diaz0David Gomez-Castro1Tatiana A. Shaposhnikova2Maria N. Zubova3 Univ. Complutense de Madrid, Spain Univ. Complutense de Madrid, Spain Moscow State Univ., Moscow, Russia Moscow State Univ., Moscow, Russia Our main interest in this article is the study of homogenized limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with periodically place particles. We focus on the case of particles (or holes) of critical diameter with respect to the period of the structure. Our main result proves the weak convergence of the sequence of solutions of the original problem to the solution of a reaction-diffusion parabolic problem containing a "strange term". The novelty of our result is that this term is a nonlocal memory solving an ODE. We prove that the resulting system satisfies a comparison principle.http://ejde.math.txstate.edu/Volumes/2019/77/abstr.htmlCritically scaled homogenizationperforated mediadynamical boundary conditionsstrange termnonlocal memory reaction |
| spellingShingle | Jesus Ildefonso Diaz David Gomez-Castro Tatiana A. Shaposhnikova Maria N. Zubova A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions Electronic Journal of Differential Equations Critically scaled homogenization perforated media dynamical boundary conditions strange term nonlocal memory reaction |
| title | A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| title_full | A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| title_fullStr | A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| title_full_unstemmed | A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| title_short | A nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| title_sort | nonlocal memory strange term arising in the critical scale homogenization of diffusion equations with dynamic boundary conditions |
| topic | Critically scaled homogenization perforated media dynamical boundary conditions strange term nonlocal memory reaction |
| url | http://ejde.math.txstate.edu/Volumes/2019/77/abstr.html |
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