On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary

Carregando...
Imagem de Miniatura

Data

2017-03-01

Título da Revista

ISSN da Revista

Título de Volume

Editor

Resumo

This paper concerns with the heat equation in the half-space ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a well-posedness result that allows us to consider critical potentials with infinite many singularities and anisotropy. Motivated by potential profiles of interest, the analysis is performed in weak Lp-spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in ℝ+n. Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis Oxn⃗.

Descrição

Palavras-chave

Heat equation, Lorentz spaces, Nonlinear boundary conditions, Self-similarity, Singular potentials, Symmetry

Como citar

Potential Analysis, v. 46, n. 3, p. 589-608, 2017.