Analysis utilizes integro-differential inequalities to derive spatial decay characteristics, suggesting implications for biharmonic operator behavior.
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.
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Shi et al. (2025) studied this question.
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