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Stability Analysis of Second-Order Linear PDEs on Time Scales

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  • Ruihong Liu
  • Chuan Zhang
  • Xianfu Zhang
  • Fanwei Meng
  • Hao Zhang
  • Chunrui Zhang

Abstract

This paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient conditions for exponential stability are strictly obtained, and the results are generalized for that where both the discrete-time and continuous-time cases are considered jointly. In addition, the theoretical results are applied to exponential synchronization of reaction-diffusion neural networks (RDNNs). Simulation examples are given to verify the feasibility of our results.

Suggested Citation

  • Ruihong Liu & Chuan Zhang & Xianfu Zhang & Fanwei Meng & Hao Zhang & Chunrui Zhang, 2023. "Stability Analysis of Second-Order Linear PDEs on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-10, April.
    • Handle: RePEc:hin:jnddns:8226450
    DOI: 10.1155/2023/8226450
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