数学
非线性系统
数学分析
Dirichlet边界条件
波动方程
边值问题
指数稳定性
乘数(经济学)
Dirichlet分布
物理
量子力学
宏观经济学
经济
作者
George J. Bautista,J. Límaco,Leyter Potenciano‐Machado
摘要
In this paper, we prove the well‐posedness of a nonlinear wave equation coupled with boundary conditions of Dirichlet and acoustic type imposed on disjoints open boundary subsets. The proposed nonlinear equation models small vertical vibrations of an elastic medium with weak internal damping and a general nonlinear term. We also prove the exponential decay of the energy associated with the problem. Our results extend the ones obtained in previous results to allow weak internal dampings and removing the dimensional restriction . The method we use is based on a finite‐dimensional approach by combining the Faedo‐Galerkin method with suitable energy estimates and multiplier techniques.
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