Publicação: On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
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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.
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Heat equation, Lorentz spaces, Nonlinear boundary conditions, Self-similarity, Singular potentials, Symmetry
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Inglês
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Potential Analysis, v. 46, n. 3, p. 589-608, 2017.
