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

Electronic Journal of Differential Equations

article

Jacques Giacomoni¹  Abdelhamid Gouasmia²  Abdelhafid Mokrane² 

[1] Université de Pau et des Pays de l'Adour, CNRS, E2S LMAP ,(UMR 5142), IPRA Avenue de l'Université-F-64013 Pau;Laboratoire d'équations aux dérivées partielles non linéaires et histoire des mathématiques École Nationale Supérieure

关键词: Fractional p-Laplace equation;    doubly nonlinear evolution equation;    Picone identity;    stabilization;    nonlinear semi-group theory.;   

DOI  :  10.58997/ejde.2021.09

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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

【 授权许可】

CC BY