SELF-SIMILAR SOLUTIONS FOR A SUPERDIFFUSIVE HEAT EQUATION WITH GRADIENT NONLINEARITY

This article studies the existence, stability, self-similarity and symmetries of solutions for a superdiffusive heat equation with superlinear and gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type spaces. Unlike in previous works on such time-fractional partial differential equations of order alpha is an element of (1, 2), we take non null initial velocities into consideration, where new difficulties arise from. We overcome them by developing an appropriate decomposition of the two-parametric Mittag-Leffier function to obtain Mikhlin-type estimates and obtain our existence theorem.