Global and local existence of solutions for nonlinear systems of time-fractional diffusion equations

Fuente: arXiv
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Main Authors: Feng, Dian, Yamamoto, Masahiro
Format: Preprint
Published: 2024
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author Feng, Dian
Yamamoto, Masahiro
author_facet Feng, Dian
Yamamoto, Masahiro
contents In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the existence of solutions global in time and the blow-up. Our approach involves the truncation of the nonlinear terms, which enables us to handle all local Lipschitz continuous nonlinear terms, provided their sum is less than or equal to zero. By employing a comparison principle for the corresponding linear system, we establish also the non-negativity of the nonlinear system.
format Preprint
id arxiv_https___arxiv_org_abs_2405_16462
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global and local existence of solutions for nonlinear systems of time-fractional diffusion equations
Feng, Dian
Yamamoto, Masahiro
Analysis of PDEs
In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the existence of solutions global in time and the blow-up. Our approach involves the truncation of the nonlinear terms, which enables us to handle all local Lipschitz continuous nonlinear terms, provided their sum is less than or equal to zero. By employing a comparison principle for the corresponding linear system, we establish also the non-negativity of the nonlinear system.
title Global and local existence of solutions for nonlinear systems of time-fractional diffusion equations
topic Analysis of PDEs
url https://arxiv.org/abs/2405.16462