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

Jincheng Shi and Yiwu Lin ()
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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

Mathematics, 2025, vol. 13, issue 17, 1-19

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.

Keywords: decay estimates; evolution equation; Saint-Venant principle; integro-differential inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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