Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping

IF 0.7 3区数学 Q2 MATHEMATICS Semigroup Forum Pub Date : 2024-03-22 DOI:10.1007/s00233-024-10419-9

Zayd Hajjej

引用次数: 0

Abstract

We study a nonlinear Cauchy problem modeling the motion of an extensible beam

$$\begin{aligned} \vert y_t\vert ^{r}y_{tt}{} & {} +\gamma \Delta ^2 y_{tt}+\Delta ^2y-\left( a+b\vert \vert \nabla y\vert \vert ^2+c (\nabla y, \nabla y_t)\right) \Delta y\\{} & {} \quad +\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \end{aligned}$$

in a bounded domain of $\mathbb {R}^N$, with clamped boundary conditions in either cases: when $r=\gamma =0$ or else when r and $\gamma $ are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy.

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具有 Balakrishnan-Taylor、强和局部非线性阻尼的可扩展梁方程的指数稳定性

我们研究了一个模拟可伸展梁运动的非线性考奇问题 $$\begin{aligned}\vert y_t\vert ^{r}y_{tt}{} & {}+\gamma \Delta ^2 y_{tt}+\Delta ^2y-\left( a+b\vert \vert \vert \vert ^2+c (\nabla y, \nabla y_t)\right) \Delta y\{} & {}\quad +\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \end{aligned}$$ in a bounded domain of $\mathbb {R}^N$, with clamped boundary conditions in either cases: when $r=\gamma =0$ or else when r and$\gamma $ are positive.在这两种情况下，我们都证明了解的存在和能量的指数衰减。

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

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

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