Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces

TL;DR

This paper proves the existence of solutions for fractional semilinear parabolic equations within Besov-Morrey spaces, accommodating diverse initial data including distributions beyond Radon measures, and also addresses viscous Hamilton-Jacobi equations.

Contribution

It introduces new existence results for fractional parabolic equations in Besov-Morrey spaces, extending the class of initial data considered.

Findings

Existence of solutions for fractional semilinear parabolic equations in Besov-Morrey spaces.

Sufficient conditions for solutions to viscous Hamilton-Jacobi equations.

Initial data includes distributions beyond Radon measures.

Abstract

In this paper, we establish the existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces for a large class of initial data including distributions other than Radon measures. We also obtain sufficient conditions for the existence of solutions to viscous Hamilton-Jacobi equations.