Ulam-Hyers stability of a parabolic partial differential equation

Abstract

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.

Keywords

• parabolic partial differential equation
• ulam-hyers stability
• generalized ulam-hyers-rassias stability
• integral inequality
• gronwall lemma
• black-scholes equation
• 35l70
• 45h10
• 47h10