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

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4355-:d:977902
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    References listed on IDEAS

    as
    1. Soon-Mo Jung & Dorian Popa & Michael Rassias, 2014. "On the stability of the linear functional equation in a single variable on complete metric groups," Journal of Global Optimization, Springer, vol. 59(1), pages 165-171, May.
    2. 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.
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