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Spatial Decay Estimates for Solutions of a Class of Evolution Equations Containing a Biharmonic Operator

Author

Listed:
  • Jincheng Shi

    (Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China)

  • Yiwu Lin

    (Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China)

Abstract

This study delves into the spatial characteristics of solutions for a specific class of evolution equations that incorporate biharmonic operators. The process begins with the construction of an energy function. Subsequently, by employing an integro-differential inequality method, it is deduced that this energy function satisfies an integro-differential inequality. Resolving this inequality enables us to establish an estimate for the spatial decay of the solution. Ultimately, the finding affirms that the spatial exponential decay is reminiscent of Saint-Venant-type estimates.

Suggested Citation

  • Jincheng Shi & Yiwu Lin, 2025. "Spatial Decay Estimates for Solutions of a Class of Evolution Equations Containing a Biharmonic Operator," Mathematics, MDPI, vol. 13(17), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2821-:d:1740132
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