Existence and symmetries of solutions in Besov-Morrey spaces for a semilinear heat-wave type equation

TL;DR

This paper establishes the global existence, symmetry properties, and asymptotic behavior of solutions to a semilinear heat-wave equation within Besov-Morrey spaces, extending previous results to larger initial data classes.

Contribution

It introduces new global existence results for a semilinear heat-wave equation in Besov-Morrey spaces with larger initial data and investigates solution symmetries and asymptotics.

Findings

Global existence in Besov-Morrey spaces for larger initial data

Analysis of symmetries and self-similarity of solutions

Characterization of asymptotic behavior of solutions

Abstract

This paper considers a semilinear integro-differential equation of Volterra type which interpolates semilinear heat and wave equations. Global existence of solutions is showed in spaces of Besov type based in Morrey spaces, namely Besov-Morrey spaces. Our initial data is larger than the previous works and our results provide a maximal existence class for semilinear interpolated heat-wave equation. Some symmetries, self-similarity and asymptotic behavior of solutions are also investigated in the framework of Besov-Morrey spaces.