| Title:
|
Existence of weak solutions to doubly degenerate diffusion equations (English) |
| Author:
|
Matas, Aleš |
| Author:
|
Merker, Jochen |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
43-69 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove existence of weak solutions to doubly degenerate diffusion equations \begin {equation*} \dot {u} = \Delta _p u^{m-1} + f \quad (m,p \ge 2) \end {equation*} by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains $\Omega \subset \mathbb R^n$ with Dirichlet or Neumann boundary conditions. The function $f$ can be an inhomogeneity or a nonlinearity involving terms of the form $f(u)$ or $\div (F(u))$. In the appendix, an introduction to weak differentiability of functions with values in a Banach space appropriate for doubly nonlinear evolution equations is given. (English) |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
doubly nonlinear evolution equation |
| Keyword:
|
weak solution |
| MSC:
|
35A01 |
| MSC:
|
35D30 |
| MSC:
|
35K20 |
| MSC:
|
35K59 |
| MSC:
|
35K65 |
| MSC:
|
35K92 |
| MSC:
|
37L65 |
| idZBL:
|
Zbl 1249.35194 |
| idMR:
|
MR2891305 |
| DOI:
|
10.1007/s10492-012-0004-0 |
| . |
| Date available:
|
2012-01-09T19:25:07Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141818 |
| . |
| Reference:
|
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| . |
