Existence and global behavior of weak solutions to a doubly nonlinear evolution fractional p-Laplacian equation
MetadataShow full metadata
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.
CitationGiacomoni, J., Gouasmia, A., & Mokrane, A. (2021). Existence and global behavior of weak solutions to a doubly nonlinear evolution fractional p-Laplacian equation. Electronic Journal of Differential Equations, 2021(09), pp. 1-37.
This work is licensed under a Creative Commons Attribution 4.0 International License.