Existence, symmetries, and asymptotic properties of global solutions for a fractional diffusion equation with gradient nonlinearity

Abstract

This work gives sufficient conditions to obtain the existence, positivity, symmetry, asymptotic and spatial behaviors of global solutions of a fractional reaction-diffusion equation with power-type and gradient nonlinearities. Eventually, we obtain results of the fractional viscous Hamilton-Jacobi equation.This article is part of the section ''Theory of PDEs'' edited by Eduardo Teixeira.