Exponential Stabilization of a Semi Linear Third Order in Time Equation with Memory

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-05-27 DOI:10.1007/s00245-024-10144-3

M. Barbosa da Silva, V. N. Domingos Cavalcanti, E. H. Gomes Tavares, T. Saito Tavares

引用次数: 0

Abstract

We are concerned with a third order in time equation in the presence of viscoelastic effects given by the memory term and with a semi linear source term, posed on a bounded domain \(\Omega \subset \mathbb {R}^3 \). Considering three different types of memory in the past history framework, we prove the well-posedness of its solutions as well as the exponential stability of the energy functional. Relaxing some hypotheses on the memory kernel, we improve and extend the results established in the existing literature.

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带记忆的半线性三阶时间方程的指数稳定

我们关注的是存在由记忆项和半线性源项给出的粘弹性效应的三阶时间方程，该方程在有界域 \(\Omega \subset \mathbb {R}^3 \)上求解。考虑到过去历史框架中三种不同类型的记忆，我们证明了其解的良好拟合性以及能量函数的指数稳定性。通过放宽对记忆核的一些假设，我们改进并扩展了现有文献中建立的结果。

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.