An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition
| Autor: | Quittner, Pavol |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions defined for all times $t\in(-\infty,\infty)$) guarantee optimal estimates of solutions of related initial-boundary value problems in general domains. We prove an optimal Liouville theorem for the linear equation in the halfspace complemented by the nonlinear boundary condition $\partial u/\partial\nu=u^q$, $q>1$. |
| Databáze: | arXiv |
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