Abstract
AbstractIn this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.
Highlights
Introduction and statement of the resultIn 1940, S
Since there has been an intense study of stability problems with emphasis on different disciplines, they are usually called Hyers-Ulam stability problems
In this paper we study the Hyers-Ulam stability of nonautonomous semilinear reaction-diffusion equations with fractional Laplacian diffusion using a convenient version of the Gronwall inequality
Summary
The Hyers-Ulam stability problem for partial differential equations is a well-known topic, see for example [2,3,4,5] and references therein. The fundamental role that Gronwall-type inequalities play in the study of the Hyers-Ulam stability problem has been appreciated, an example of such a fact can be seen in [11,12]. Ten equivalent definitions of fractional Laplacian are presented in [13]; in the books [14,15] we usually find the most relevant properties of such an integral operator This background motivates the present work, apart from the fact, to the best of our knowledge, that there are no previous results studying the Hyers-Ulam stability problem for equations of the type considered here.
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