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

• Main Authors: Jacques Giacomoni, Abdelhamid Gouasmia, Abdelhafid Mokrane
• Format: Article
• Language: English
• Published: Texas State University 2021-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: fractional p-laplace equation; doubly nonlinear evolution equation; picone identity; stabilization; nonlinear semi-group theory
• Online Access: http://ejde.math.txstate.edu/Volumes/2021/09/abstr.html

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.