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

Abstract

<p style='text-indent:20px;'>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.</p>

Source identification problems for abstract semilinear nonlocal differential equations

“…This assumption has been used in a lots of works recently, e.g. [16,17,28,30,33,34]. The uniqueness of l in this assumption is shown in [6,Theorem 5.2,p.158].…”