SELF-SIMILARITY, SYMMETRIES AND ASYMPTOTIC BEHAVIOR IN MORREY SPACES FOR A FRACTIONAL WAVE EQUATION

摘要

This paper is concerned with a fractional PDE that interpolates semilinear heat and wave equations. We show results on global-intime well-posedness for small initial data in the critical Morrey spaces and space dimension n ≥ 1. We also remark how to derive the localin-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.