An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition

Pavol Quittner

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arXiv · 2009.13923

An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition

Pavol Quittner

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Abstract

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 $\partial u/\partialν=u^q$, $q>1$.

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Pavol Quittner. 2020-09-29. An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition. https://arxiv.org/abs/2009.13923

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