Antontsev, Stansislav; Chipot, Michel; Shmarev, Sergey (2013). Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure and Applied Analysis, 12(4):1527-1546.
The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div (a(x, t, u)|u|α(x, t)|∇u|p(x, t)-2 with given variable exponents α(x, t) and p(x, t). We establish conditions on the data which guarantee the comparison principle and uniqueness of bounded weak solutions in suitable function spaces of Orlicz-Sobolev type.
The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div (a(x, t, u)|u|α(x, t)|∇u|p(x, t)-2 with given variable exponents α(x, t) and p(x, t). We establish conditions on the data which guarantee the comparison principle and uniqueness of bounded weak solutions in suitable function spaces of Orlicz-Sobolev type.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | July 2013 |
| Deposited On: | 06 Dec 2013 12:11 |
| Last Modified: | 11 Dec 2023 02:37 |
| Publisher: | American Institute of Mathematical Sciences |
| ISSN: | 1534-0392 |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.3934/cpaa.2013.12.1527 |
Antontsev, Stansislav