Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

TL;DR

This paper proves the existence of solutions for a complex higher-order semilinear parabolic equation with singular initial data, introducing a new kernel and analyzing initial data conditions.

Contribution

It introduces a novel majorizing kernel and determines the minimal initial data singularity for solution existence.

Findings

Existence of solutions under new kernel framework

Necessary conditions on initial data for local solutions

Identification of the strongest initial data singularity

Abstract

We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.