Abstract
This paper concerns with the heat equation in the half-space \(\mathbb {R}_{+}^{n}\) with nonlinearity and singular potential on the boundary \(\partial \mathbb {R}_{+}^{n}\). 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 L p-spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in \(\mathbb {R}_{+}^{n}\). Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis \(\overrightarrow {Ox_{n}}\).
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L. Ferreira was supported by FAPESP and CNPQ, Brazil.
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de Almeida, M.F., Ferreira, L.C.F. & Precioso, J.C. On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary. Potential Anal 46, 589–608 (2017). https://doi.org/10.1007/s11118-016-9595-5
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DOI: https://doi.org/10.1007/s11118-016-9595-5