Artículos de revistas
On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
Fecha
2017-03-01Registro en:
Potential Analysis, v. 46, n. 3, p. 589-608, 2017.
1572-929X
0926-2601
10.1007/s11118-016-9595-5
2-s2.0-84988736508
2-s2.0-84988736508.pdf
Autor
Universidade Federal de Sergipe (UFS)
Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
Institución
Resumen
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.