Nonlinear boundary value problems relative to one dimensional heat equation

Laurent Veron (1)

1 IDP - Institut Denis Poisson

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, ∞).

Mots clés: Nonlinear heat flux; Singularities; Radon measures; Marcinkiewicz spaces

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Veron. Nonlinear boundary value problems relative to one dimensional heat equation. 2020. ⟨hal-02771254v1⟩