IJPAM: Volume 103, No. 1 (2015)

HYERS-ULAM STABILITY OF
HEAT-CONDUCTION EQUATION

Zhaohui Gu$^1$, Jinghao Huang$^2$
$^1$School of Economics & Trade
Guangdong University of Foreign Studies
Guangzhou, 510006, P.R. CHINA
Department of Mathematics
Sun Yat-Sen University
Guangzhou, 510275, P.R. CHINA


Abstract. We prove the Hyers-Ulam stability of a partial differential equation. That is, if $u$ is an approximate solution of the heat-conduction equation $\frac{\partial u}{\partial t}=a^2 \frac{\partial ^2 u}{\partial x^2}+f(x,t)$ and $\frac{\partial u}{\partial t}= a^2(\frac{\partial ^2 u}{\partial x^2}+\frac{\partial ^2 u}{\partial y^2})+f(x,y,t)$, then there exists an exact solution of the differential equation near to $u$.

Received: March 15, 2015

AMS Subject Classification: 34K20, 26D10

Key Words and Phrases: Hyers-Ulam stability, heat-conduction equation, partial differential equation

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DOI: 10.12732/ijpam.v103i1.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 71 - 80


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