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Nonlinear boundary value problems relative to one dimensional heat equation

Abstract : We consider the problem of existence of a solution u to ∂ t u − ∂ xx u = 0 in (0, T) × R + subject to the boundary condition −u x (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 ∂ t u − ∂ xx u = 0 in R + × R + such that −u x (t, 0) + u p = 0 on (0, ∞).
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https://hal.archives-ouvertes.fr/hal-02771254
Contributor : Laurent Veron <>
Submitted on : Thursday, August 20, 2020 - 11:00:13 AM
Last modification on : Monday, July 26, 2021 - 3:02:52 PM

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Laurent Veron. Nonlinear boundary value problems relative to one dimensional heat equation. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics, Università di Trieste, 2020, 52, pp.1-23. ⟨10.13137/0049-4704/xxxxx⟩. ⟨hal-02771254v3⟩

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