ABSTRACT We study the asymptotic behavior of Bresse system with non-dissipative kernel memory acting only in the equation of longitudinal displacement. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a new relationship between the coefficients of the system. Moreover, this new condition on the constants of the system is used to prove strong stability and exponential stability for the homogeneous case (frictional dissipation in the longitudinal equation).

中文翻译：

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具有无限记忆耗散的 Bresse 系统的稳定性条件

摘要 我们研究了仅作用于纵向位移方程的具有非耗散核记忆的 Bresse 系统的渐近行为。我们表明指数稳定性取决于有关内核衰减率的条件以及系统系数之间的新关系。此外，系统常数的这一新条件用于证明齐次情况（纵向方程中的摩擦耗散）的强稳定性和指数稳定性。