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

Fang Wang () and Ying Gao
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Fang Wang: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
Ying Gao: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China

Mathematics, 2022, vol. 10, issue 22, 1-10

Abstract: In this paper, we prove the Hyers–Ulam stability and generalized Hyers–Ulam stability of u t ( x , t ) = a ( t ) Δ u ( x , t ) with an initial condition u ( x , 0 ) = f ( x ) for x ∈ R n and 0 < t < T ; 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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