A comparison principle for a class of doubly nonlinear parabolic fractional partial differential equations

Abstract

In this paper, we establish a comparison principle for non-negative weak solutions to a class of doubly nonlinear parabolic fractional partial differential equations within a space-time cylinder ${\Omega }_T=\Omega \times (0,T)\subset {\mathbb{R}}^{n+1}$. For the two solutions considered, we assume that at least one of them is time-independent outside the spatial domain, i.e. in ${\Omega }^c={\mathbb{R}}^n\setminus \Omega$. As an application of this result, we readily infer the uniqueness of a non-negative weak solution to the corresponding Cauchy-Dirichlet problem.