This paper studies the existence of weak solutions and their asymptotic behaviour to the initial boundary value problem for a multidimensional nonlinear Bresse system. The existence of the solutions of the problem is obtained by appliying Galerkin method. Then, we obtain an explicit decay rate estimation dependent on both the strain-caused stress and the damping terms by using the multiplier method with integral.

中文翻译：

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具有时变耗散的新型多维非线性Bresse系统的衰减率估计

本文研究了多维非线性Bresse系统初始边界值问题的弱解的存在性及其渐近性。问题的解决方案的存在是通过应用Galerkin方法获得的。然后，通过使用带积分的乘数方法，我们获得了一个既取决于应变引起的应力又取决于阻尼项的显式衰减率估计。