Global existence and stabilization of the quasilinear Petrovsky equation with localized nonlinear damping

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-26 DOI:10.1016/j.jmaa.2024.129087

Bochra Belhadji , Mama Abdelli , Akram Ben Aissa , Khaled Zennir

引用次数: 0

Abstract

We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.

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具有局部非线性阻尼的准线性彼得罗夫斯基方程的全局存在性和稳定性

我们考虑了有界域中的局部非线性阻尼板方程，其中阻尼仅在边界的适当子集附近有效。利用 Faedo-Galerkin 方法，我们证明了全局解的存在性和唯一性。在适当假设阻尼局部化的几何条件下，我们通过引入合适的 Lyapunov 函数建立了解的指数稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.