Differential and Integral Equations

Self-similarity, symmetries and asymptotic behavior in Morrey spaces for a fractional wave equation

Abstract

This paper is concerned with a fractional PDE that interpolates semilinear heat and wave equations. We show results on global-in-time well-posedness for small initial data in the critical Morrey spaces and space dimension $n\geq1$. We also remark how to derive the local-in-time version of the results. Qualitative properties of solutions like self-similarity, antisymmetry and positivity are also investigated. Moreover, we analyze the asymptotic stability of the solutions and obtain a class of asymptotically self-similar solutions.

Article information

Source
Differential Integral Equations Volume 25, Number 9/10 (2012), 957-976.

Dates
First available in Project Euclid: 20 December 2012