2020
DOI: 10.48550/arxiv.2007.13391
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Singular solutions for fractional parabolic boundary value problems

Abstract: The standard problem for the classical heat equation posed in a bounded domain Ω of R n is the initial and boundary value problem. If the Laplace operator is replaced by a version of the fractional Laplacian, the initial and boundary value problem can still be solved on the condition that the nonzero boundary data must be singular, i.e., the solution u(t, x) blows up as x approaches ∂Ω in a definite way. In this paper we construct a theory of existence and uniqueness of solutions of the parabolic problem with … Show more

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