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arXiv · 2109.01567

Existence theory of the nonlinear plate equations

Carlos Banquet·Gilmar Garbugio·Élder J. Villamizar-Roa
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Abstract

This paper is devoted to the theoretical analysis of the nonlinear plate equations in $\mathbb{R}^{n}\times (0,\infty),$ $n\geq1,$ with nonlinearity involving a type polynomial behavior. We prove the existence and uniqueness of global mild solutions for small initial data in $L^{1}(\mathbb{R}^{n})\cap H^s(\mathbb{R}^{n})$-spaces. We also prove the existence and uniqueness of local and global solutions in the framework of Bessel-potential spaces $H^s_p(\mathbb{R}^n)=(I-Δ)^{s/2}L^p(\mathbb{R}^n).$ In order to derive the existence results we develop new time decay estimates of the solution of the corresponding linear problem.

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Carlos Banquet, Gilmar Garbugio, Élder J. Villamizar-Roa. 2021-09-03. Existence theory of the nonlinear plate equations. https://doi.org/10.1007/s00033-021-01646-z

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