Electron. J. Differential Equations, Vol. 2021 (2021), No. 09, pp. 1-37.
Existence and global behavior of weak solutions to a doubly nonlinear evolution
fractional p-Laplacian equation
Jacques Giacomoni, Abdelhamid Gouasmia, Abdelhafid Mokrane
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.
DOI: https://doi.org/10.58997/ejde.2021.09
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Jacques Giacomoni
Université de Pau et des Pays de l'Adour,
CNRS, E2S LMAP (UMR 5142), IPRA
Avenue de l'Université-F-64013 Pau, France
email: jacques.giacomoni@univ-pau.fr
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Abdelhamid Gouasmia
Laboratoire d'équations aux dérivées partielles non linéaires et histoire des
mathématiques
École Nationale Supérieure, B.P. 92
Vieux Kouba, 16050 Algiers, Algeria
email: gouasmia.abdelhamid@gmail.com
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Abdelhafid Mokrane
Laboratoire d'équations aux dérivées partielles non linéaires et histoire des
mathématiques
École Nationale Supérieure, B.P. 92
Vieux Kouba, 16050 Algiers, Algeria
email: abdelhafid.mokrane@ens-kouba.dz
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