具有时滞的非线性多孔弹性系统的指数稳定性
Exponential stability for a nonlinear porous-elastic system with delay
AI总结：
针对带时滞的非线性多孔弹性系统，利用半群理论及Lyapunov泛函，在系数关系下证明了全局解存在唯一及能量指数衰减。
摘要：
本文研究了一类具有时滞的非线性多孔弹性系统全局解的存在性及能量的指数衰减。非线性项和时滞作用于体积分数方程中。为获得全局解的存在唯一性，我们将利用线性算子的半群理论，并在涉及系统系数的特定关系下，结合Lyapunov泛函，建立系统能量的指数衰减。
英文摘要：
In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to obtain the existence and uniqueness of a global solution, we will use the semigroup theory of linear operators and under a certain relation involving the coefficients of the system together with a Lyapunov functional, we will establish the exponential decay of the energy associated to the system.
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