Existence of weak solutions of doubly nonlinear parabolic equations
| Autor: | Stefan Sturm |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Boundary (topology) Cantor function 01 natural sciences 010101 applied mathematics Nonlinear parabolic equations symbols.namesake Homogeneous symbols Cylinder Boundary value problem Limit (mathematics) 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 455:842-863 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.06.024 |
| Popis: | We deal with a Cauchy–Dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space–time cylinder for doubly nonlinear parabolic equations, whose prototype is ∂ t u − div ( | u | m − 1 | D u | p − 2 D u ) = f with a non-negative Lebesgue function f on the right-hand side, where p > 2 n n + 2 and m > 0 . The central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f. The constructed solution is obtained by a limit of approximations, i.e. we use solutions of regularized Cauchy–Dirichlet problems and pass to the limit to receive a solution for the original Cauchy–Dirichlet problem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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