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

Villa-Morales José

Demonstratio Mathematica

2020

Vol. 53, nr 1

269--276

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.

Ulam-Hyers stability of a parabolic partial differential equation

Marian Daniela, Ciplea Sorina Anamaria, Lungu Nicolaie

Demonstratio Mathematica

2019

Vol. 52, nr 1

475--481

The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.

Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem

Khorshidi M. N., Yousefi S. A.

Journal of Applied Analysis

2016

Vol. 22, nr 2

169--179

An inverse problem concerning a diffusion equation with source control parameter is considered. The approximation of the problem is based on the Ritz method with satisfier function. The Ritz method together with the least squares approximation (Ritz-least squares method) are utilized to reduce the inverse problem to the solution of algebraic equations. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique.