Existence and global behavior of weak solutions to a doubly nonlinear evolution fractional p-Laplacian equation
Date
2021-02-23
Authors
Giacomoni, Jacques
Gouasmia, Abdelhamid
Mokrane, Abdelhafid
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Fractional p-Laplace equation, Doubly nonlinear evolution equation, Picone identity, Stabilization, Nonlinear semi-group theory
Citation
Giacomoni, J., Gouasmia, A., & Mokrane, A. (2021). Existence and global behavior of weak solutions to a doubly nonlinear evolution fractional p-Laplacian equation. <i>Electronic Journal of Differential Equations, 2021</i>(09), pp. 1-37.
Rights
Attribution 4.0 International