For the one-dimensional gas dynamics in thermal nonequilibrium which is a \(4\times 4\) nonlinear hyperbolic system with relaxation, global existence for Cauchy problem is established, and the asymptotic stability of the traveling wave solution with shock profile is proved under the condition that the shock strength and the initial disturbance are small and the integral zero of the initial disturbance.

中文翻译：

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热非平衡中气体动力学系统行波的非线性渐近稳定性

对于具有松弛的\（4×4）非线性双曲系统，在热非平衡中的一维气体动力学，建立了柯西问题的整体存在性，并证明了在冲击波作用下行波解的渐近稳定性。冲击强度和初始扰动较小且初始扰动为零的条件。