Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion

Abstract

In 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.

Keywords

• parabolic partial differential equations
• hyers-ulam stability
• fractional laplacian
• gronwall type inequalities
• 35b20
• 35b35
• 45h05
• 47h10