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 \(\partial u/\partial \nu =u^q\), \(q>1\).
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Supported in part by the Slovak Research and Development Agency under the contract No. APVV-18-0308 and by VEGA grant 1/0347/18.
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Dedicated to the memory of Pavol Brunovský
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Quittner, P. An Optimal Liouville Theorem for the Linear Heat Equation with a Nonlinear Boundary Condition. J Dyn Diff Equat 36 (Suppl 1), 53–63 (2024). https://doi.org/10.1007/s10884-020-09917-5
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DOI: https://doi.org/10.1007/s10884-020-09917-5