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

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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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  • 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.

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

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