In this paper, we consider a semilinear Bresse system in one dimensional bounded non homogeneous medium. We investigate stability issues for such a problem with a nonlinear damping acting in all three wave equations. We prove, firstly, the existence and uniqueness of the solutions by using the nonlinear semigroup method. Afterwords, we establish an uniform decay rates of the energy for these solutions without considering any restriction on the coefficients as well as the equality of the wave propagation speeds. Some techniques of the microlocal analysis theory are used in order to reach the desired asymptotics.

中文翻译：

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具有变系数和局部分布非线性耗散的半线性 Bresse 系统的渐近行为

在本文中，我们考虑一维有界非齐次介质中的半线性布雷斯系统。我们研究了非线性阻尼作用于所有三个波动方程的问题的稳定性问题。我们首先用非线性半群方法证明了解的存在性和唯一性。之后，我们为这些解建立了统一的能量衰减率，而不考虑对系数的任何限制以及波传播速度的相等性。使用微局域分析理论的一些技术来达到所需的渐进性。