Existence of solutions for an inhomogeneous fractional semilinear heat\n equation

2019/10/26 by Kotaro Hisa, Kazuhiro Ishige, Hisa, Kotaro +3 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1910.12013

Abstract

We obtain necessary conditions and sufficient conditions on the existence of\nsolutions to the Cauchy problem for a fractional semilinear heat equation with\nan inhomogeneous term. We identify the strongest spatial singularity of the\ninhomogeneous term for the solvability of the Cauchy problem.\n

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• Solvability of inhomogeneous fractional semilinear heat equations in Lorentz--Morrey spaces

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