Existence of solutions for an inhomogeneous fractional semilinear heat equation

TL;DR

This paper investigates the conditions under which solutions exist for an inhomogeneous fractional semilinear heat equation, focusing on the impact of spatial singularities of the inhomogeneous term.

Contribution

It provides necessary and sufficient conditions for solution existence, highlighting the critical spatial singularity affecting solvability.

Findings

Identifies the strongest spatial singularity allowing solutions.

Establishes criteria for existence based on inhomogeneous term properties.

Clarifies the role of inhomogeneity in fractional heat equations.

Abstract

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