Stability of initial-boundary value problem for diffusion equation on a half space

Abstract

In this paper, Hyers–Ulam stability of the diffusion equation on the half space ${\mathbb{R}}_{+}^{n+1}$ with $n\ge 2$ is investigated: $\frac{\mathrm{\partial }u}{\mathrm{\partial }t}(x,y,t)=△u(x,y,t)$ where $x\in {\mathbb{R}}^n$, y>0, and t>0. Using integral transforms, precisely, Fourier transform with respect to the tangential space x and Laplace transform for time t, we obtain the generalized Hyers–Ulam stability of diffusion equation in the half space ${\mathbb{R}}_{+}^{n+1}$ involving special functions such as gamma and error functions.

Keywords:

• Hyers–Ulam stability
• Laplace equations
• Fourier transforms
• gamma functions
• error functions

AMS CLASSIFICATIONs:

• 39B52
• 35A22
• 42A38

Disclosure statement

No potential conflict of interest was reported by the author(s).