Existence and uniqueness of solution for some time fractional parabolic equations involving the 1-Laplace operator

Claudianor O. Alves () and Tahir Boudjeriou ()
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Claudianor O. Alves: Unidade Acadêmica de Matemática Universidade Federal de Campina Grande
Tahir Boudjeriou: Institute of Electrical and Electronic Engineering University of Boumerdes

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-35

Abstract: Abstract This paper is devoted to study the time fractional parabolic 1-Laplacian type. Firstly, by using the parabolic regularization technique and approximating the parabolic 1-Laplacian problem by a class of parabolic equations of p-Laplacian type with $$p>1$$ p > 1 , we establish the existence of global weak radial solutions to the considered problem for a wide class of nonlinearities. Secondly, we discuss the extinction property of solutions to the time fractional total variation flow (FTVF) with different boundary conditions (Dirichlet and Neumann conditions). We conclude this paper by providing an example of explicit solution to the (FTVF).

Keywords: Time fractional parabolic equations; Degenerate parabolic equations; Extinction time; 34K37; 47J35; 35K55; 65N30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-022-00222-y

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