Uniform Stabilization for the Semi-linear Wave Equation with Nonlinear Kelvin–Voigt Damping

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-10-06 DOI:10.1007/s00245-024-10186-7

Kaïs Ammari, Marcelo M. Cavalcanti, Sabeur Mansouri

引用次数: 0

Abstract

This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin–Voigt type which is distributed around a neighborhood of the boundary and the second is a frictional damping depending in the first one. We show uniform decay rate results of the corresponding energy for all initial data taken in bounded sets of finite energy phase-space. The proof is based on obtaining an observability inequality which combines unique continuation properties and the tools of the Microlocal Analysis Theory

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具有非线性开尔文-沃依格阻尼的半线性波方程的均匀稳定问题

本文关注的是在有界域中受到两个局部阻尼作用的半线性波方程解的衰减估计。第一个阻尼属于非线性开尔文-沃伊特类型，分布在边界附近；第二个阻尼属于摩擦阻尼，取决于第一个阻尼。我们展示了有限能量相空间有界集中所有初始数据相应能量的均匀衰减率结果。证明基于可观测性不等式，该不等式结合了独特的延续特性和微局域分析理论工具。

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

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.