Existence and global behavior of weak solutions to a doubly nonlinear evolution fractional p-Laplacian equation

Abstract

In this article, we study a class of doubly nonlinear parabolic problems involving the fractional p-Laplace operator. For this problem, we discuss existence, uniqueness and regularity of the weak solutions by using the time-discretization method and monotone arguments. For global weak solutions, we also prove stabilization results by using the accretivity of a suitable associated operator. This property is strongly linked to the Picone identity that provides further a weak comparison principle, barrier estimates and uniqueness of the stationary positive weak solution.

Keywords

• fractional p-laplace equation
• doubly nonlinear evolution equation
• picone identity
• stabilization
• nonlinear semi-group theory