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A Dilation Invariance Method and the Stability of Inhomogeneous Wave Equations

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  • Ginkyu Choi

    (Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, Sejong 30016, Korea)

  • Soon-Mo Jung

    (Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea)

Abstract

We apply the method of a kind of dilation invariance to prove the generalized Hyers-Ulam stability of the (inhomogeneous) wave equation with a source, u t t ( x , t ) − c 2 ▵ u ( x , t ) = f ( x , t ) , for a class of real-valued functions with continuous second partial derivatives in each of spatial and the time variables.

Suggested Citation

  • Ginkyu Choi & Soon-Mo Jung, 2019. "A Dilation Invariance Method and the Stability of Inhomogeneous Wave Equations," Mathematics, MDPI, vol. 7(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:70-:d:196444
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    References listed on IDEAS

    as
    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, June.
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    Cited by:

    1. Fang Wang & Ying Gao, 2022. "The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient," Mathematics, MDPI, vol. 10(22), pages 1-10, November.

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