On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations

Dinh-Ke Tran; Nhu-Thang Nguyen

doi:10.3934/cpaa.2021200

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2022, Volume 21, Issue 3: 817-835. Doi: 10.3934/cpaa.2021200

This issue Previous Article Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities Next Article Radial symmetry of nonnegative solutions for nonlinear integral systems

On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations

Dinh-Ke Tran^, and
Nhu-Thang Nguyen

Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

^* Corresponding author
^* Corresponding author

Received: August 2021

Early access: December 2021

Published: March 2022

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2020.07. The first author was also supported by the Vietnam Institute for Advanced Study in Mathematics-VIASM

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Abstract

We study a class of nonlocal partial differential equations with nonlinear perturbations, which is a general model for some equations arose from fluid dynamics. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and stability of solutions. Our analysis is based on the theory of completely positive kernel functions, local estimates and a new Gronwall type inequality.

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Mathematics Subject Classification: Primary: 35B40, 35B65; Secondary: 35C15, 45K05.

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