On a Class of Nonlinear Plate Equations on Modulation Spaces

作     者：Banquet, Carlos Corpa-Linan, Luis Villamizar-Roa, elder J. 

作者机构：Univ Cordoba Dept Matemat & Estadist AA 354 Monteria Colombia Univ Ind Santander Escuela Matemat AA 678 Bucaramanga Colombia 

出 版 物：《POTENTIAL ANALYSIS》 (Potential Anal.)

年 卷 期：2025年

页      面：1-28页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Universidad de Cordoba [FCB-05-22] Vicerrectoria de Investigacion y Extension of Universidad Industrial de Santander Project "Controllability and Inverse Problems in Free Boundary Problems for incompressible Fluids-CIPIF"- MATH-AmSud-2022 

主　　题：Plate equations Modulation spaces Time-decay estimates Global solutions Stability 

摘      要：This paper is devoted to the study of the initial value problem for a nonlinear plate equation in Rnx(0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}n\times (0,\infty )$$\end{document} with initial data in modulation spaces, which includes the Bessel-potential Hps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H{s}_p$$\end{document} and Besov spaces Bp,qs,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B{s}_{p,q},$$\end{document} for large regularity indexes s. We derive a set of time-decay estimates for the corresponding linear plate equation on the framework of modulation spaces, and then, we use these results to analyze the existence and asymptotic stability of global solutions of the nonlinear problem.