Work

On the solutions to variable-order fractional $ p $ -Laplacian evolution equation with $ L^1 $ -data

Year: 2025

Type: article

Abstract: This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $ L^1 $-data, which has a variable-order fractional $ p $-Laplacian operator. The existence and uniqueness of renormalized solutions and entropy solutions to the equation is proved. To address the significant challenges encountered during this process, we use approximation and energy methods. In the process of proving, the well-posedness of weak solutions to the problem has been established initially, while also establishing a comparative result of solutions.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025086

Authors: Sixuan Liu, Gang Dong, Hui Bi, Boying Wu

Institutions: Harbin University of Science and Technology, Harbin Institute of Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G5954515037