The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient

Abstract

In this paper, we prove the Hyers–Ulam stability and generalized Hyers–Ulam stability of ut(x,t)=a(t)Δu(x,t) with an initial condition u(x,0)=f(x) for x∈Rn and 0tT; the corresponding conclusions of the standard heat equation can be also derived as corollaries. All of the above results are proved by using the properties of the fundamental solution of the equation.

Keywords

• generalized Hyers–Ulam stability
• Hyers–Ulam stability
• heat equations with time-dependent coefficient
• fundamental solutions