Nonlinear boundary value problems relative to one dimensional heat equation

2020/06/05 by Veron, Laurent
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.03335

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,∞). At end, we present various extensions to a higher dimensional framework.

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