Nonlinear boundary value problems relative to the one dimensional heat equation

Véron, Laurent
2020
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ISSN
0049-4704
DOI
e-ISSN
2464-8728
Abstract
We consider the problem of existence of a solution u to δtu — δxxu = 0 in (0, T) x R+ subject to the boundary condition — ux(t,0) + g(u(t, 0)) = μ on (0, T) where μ is a measure on (0, T) and g a continuous nondecreasing function. When p > 1 we study the set of self-similar solutions of δtu — δxxu = 0 in R+ — R+ such that —ux(t,0)+up = 0 on (0,∞). At end, we present various extensions to a higher dimensional framework.
Journal
Subjects
Publisher
EUT Edizioni Università di Trieste
Source
Laurent Véron, "Nonlinear boundary value problems relative to the one dimensional heat equation" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Licence