发表机构
University of Sharjah; American University of Ras Al Khaimah（沙迦大学; 拉斯海马美国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究部分对数阻尼波动系统的全局存在性与能量衰减，提出利用Faedo-Galerkin逼近和非Lipschitz对数非线性单调性证明强解存在，并在交叉耦合约束下证明能量渐近衰减。
AI 中文摘要
我们研究了一个在有界域中由两个波动方程组成的弱耦合演化系统的全局存在性和能量衰减性质。该系统表现出一种独特的结构不对称性：一个非线性对数阻尼项仅作为类摩擦反馈机制作用于第一个波动方程，而第二个方程完全没有阻尼，仅依靠线性交叉耦合来传递和耗散其能量。我们确立了两个主要目标。首先，通过利用Faedo-Galerkin逼近方案以及非Lipschitz对数非线性的结构单调性性质，我们证明了强解的一个严格的全局存在性结果。其次，我们提供了一个严格的数学证明，展示了在交叉耦合参数的适当约束下解的稳定性和渐近能量衰减。这些结果为退化非线性阻尼下耦合双曲系统的稳定化机制提供了新的见解。
英文摘要
We investigate the global existence and energy decay properties of a weakly coupled evolution system consisting of two wave equations in a bounded domain. The system exhibits a unique structural asymmetry: a nonlinear logarithmic damping term acts exclusively as a friction-like feedback mechanism on the first wave equation, while the second equation remains completely undamped and relies solely on linear cross-coupling to transfer and dissipate its energy. We establish two primary objectives. First, by utilizing the Faedo-Galerkin approximation scheme in conjunction with the structural monotonicity properties of the non-Lipschitz logarithmic nonlinearity, we prove a rigorous global existence result for strong solutions. Second, we provide a rigorous mathematical proof demonstrating the stability and asymptotic energy decay of the solutions under suitable constraints on the cross-coupling parameter. These results provide new insights into the stabilization mechanisms of coupled hyperbolic systems under degenerate nonlinear damping.
