Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 09, pp. 1-37.

Title: Existence and global behavior of weak solutions to a doubly nonlinear evolution
       fractional p-Laplacian equation
       
Authors: Jacques Giacomoni (Univ. de Pau et des Pays de l'Adour, France)
         Abdelhamid Gouasmia (Ecole Nationale Superieure, Algiers, Algeria) 
         Abdelhafid Mokrane  (Ecole Nationale Superieure, Algiers, Algeria)

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.

Submitted June 6, 2020. Published February 23, 2021.
Math Subject Classifications: 35B40, 35K59, 35K55, 35K10, 35R11.
Key Words: Fractional p-Laplace equation; doubly nonlinear evolution equation;
           Picone identity; stabilization; nonlinear semi-group theory.