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Uniform global existence and parabolic limit for partially dissipative hyperbolic systems

机译:部分耗散双曲系统的一致全局存在性和抛物极限

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This work concerns smooth solutions to the Cauchy problem for first-order partially dissipative hyperbolic systems with a small parameter. The systems are written in non-conservative form in several space variables. We introduce algebraic conditions on the structure of the systems. Under these conditions together with a partial dissipation condition and the Shizuta Kawashima stability condition, we prove three main results around constant equilibrium states. These results are uniform global existence with respect to the parameter, global-in-time convergence of the systems to second-order nonlinear parabolic systems in a slow time variable, and global existence when the parameter is fixed. We also give examples of physical models to which the above results can be applied. (C) 2016 Elsevier Inc. All rights reserved.
机译:这项工作涉及具有小参数的一阶部分耗散双曲系统的柯西问题的光滑解。系统以非保守形式写在几个空间变量中。我们介绍系统结构的代数条件。在这些条件下以及部分耗散条件和静岛川岛稳定性条件下,我们证明了围绕恒定平衡态的三个主要结果。这些结果是关于参数的统一全局存在,在慢时间变量中系统到二阶非线性抛物系统的全局时间收敛,以及在参数固定时的全局存在。我们还给出了可以应用上述结果的物理模型的示例。 (C)2016 Elsevier Inc.保留所有权利。

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