Open AccessOn regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations
Author(s) -
Dinh-Ke Tran,
Nguyen Nhu Thang
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021200
Subject(s) - nonlinear system , mathematics , class (philosophy) , stability (learning theory) , kernel (algebra) , mathematical analysis , type (biology) , partial differential equation , dynamics (music) , gronwall's inequality , inequality , pure mathematics , physics , computer science , ecology , quantum mechanics , machine learning , artificial intelligence , acoustics , biology
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.