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

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

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,...

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Bibliographic Details
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
Description
Summary: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.
ISSN:1072-6691

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