| Title:
|
Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form (English) |
| Author:
|
Elemine Vall, Mohamed Saad Bouh |
| Author:
|
Ahmed, Ahmed |
| Author:
|
Touzani, Abdelfattah |
| Author:
|
Benkirane, Abdelmoujib |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
225-249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence of solutions to nonlinear parabolic problems of the following type: $$ \begin {cases} \dfrac {\partial b(u)}{\partial t}+ A(u) = f + {\rm div}(\Theta (x; t; u))& \text {in}\ Q,\\ u(x; t) = 0 & \text {on}\ \partial \Omega \times [0; T],\\ b(u)(t = 0) = b(u_0) & \text {on}\ \Omega , \end {cases} $$ where $b\colon \Bbb {R}\to \Bbb {R}$ is a strictly increasing function of class ${\mathcal C}^1$, the term $$ A(u) = -{\rm div} (a(x, t, u,\nabla u)) $$ is an operator of Leray-Lions type which satisfies the classical Leray-Lions assumptions of Musielak type, $\Theta \colon \Omega \times [0; T]\times \Bbb {R}\to \Bbb {R}$ is a Carathéodory, noncoercive function which satisfies the following condition: $\sup _{|s|\le k} |\Theta ({\cdot },{\cdot },s)| \in E_{\psi }(Q)$ for all $k > 0$, where $\psi $ is the Musielak complementary function of $\Theta $, and the second term $f$ belongs to $L^{1}(Q)$. (English) |
| Keyword:
|
inhomogeneous Musielak-Orlicz-Sobolev space |
| Keyword:
|
parabolic problems |
| Keyword:
|
Galerkin method |
| MSC:
|
58J35 |
| MSC:
|
65L60 |
| idZBL:
|
Zbl 06940882 |
| idMR:
|
MR3852293 |
| DOI:
|
10.21136/MB.2017.0087-16 |
| . |
| Date available:
|
2018-08-31T09:41:55Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147390 |
| . |
| Reference:
|
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