发表机构
School of Mathematics and Statistics, Nanning Normal University; School of Mathematical Sciences, Shanghai Jiao Tong University; School of Mathematical Sciences, Fudan University（南宁师范大学数学与统计学院; 上海交通大学数学科学学院; 复旦大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无等波速假设的耦合二阶发展方程系统，利用广义正定核性质，克服了不同波速及记忆核非负非增缺失等困难，获得了能量的最优多项式稳定性结果，并给出了应用。
AI 中文摘要
我们在Hilbert空间中研究了一类耦合二阶发展方程系统的稳定性，该系统具有间接一般记忆阻尼，且不满足等波速型假设，其中阻尼仅出现在一个方程中，记忆核不一定是非负且非增的，并且系统隐含的“波速”可以不同。利用新的处理思想，并借助广义正定核的性质，我们克服了由不同“波速”、记忆核缺乏递减和非负性质以及系统仅有一个方程带阻尼所带来的困难，获得了能量的最优多项式稳定性结果，该结果涵盖了文献中已有的关于二阶耦合方程（抽象或具体）的相关多项式稳定性结果。此外，我们还给出了抽象结果的应用。
英文摘要
We study the stability for a system of coupled second order evolution equations with indirect general memory-damping without the equal-wave-speeds-type hypothesis in a Hilbert space, where the damping only appears just in one equation, the memory kernel can not necessarily be nonnegative and nonincreasing, and the ``wave speeds" implied by the system can be different. Taking advantage of new processing ideas and with the help of the properties of the Generalized Positive Definite Kernel, we overcome difficulties caused by the different ``wave speeds", the lack of the decreasing and nonnegative property for the memory kernel and the system has only one equation with damping, and obtain an optimal polynomial stability result for the energy, which covers the previous related polynomial stability results for second order coupled equations (abstract or concrete) in the literature. Moreover, applications of the abstract result are given.
