Stability of Superposition of Two Viscous Shock Waves for the Boltzmann Equation

In this paper we study the time-asymptotic stability of a superposition of two viscous shock waves for one-dimensional Boltzmann equation in Eulerian coordinate under the general initial perturbation without the zero total macroscopic mass condition. Roughly speaking, the general perturbation without the zero mass condition will generate not only the shifts on the two viscous shock waves, but also the linear diffusion wave in the linearly degenerate field. Furthermore, the coupled diffusion waves for the macroscopic part are also crucial in the stability analysis. By using the delicate weighted characteristic energy estimates based on the underlying wave structure, we succeed in proving the time-asymptotic stability of a superposition of two viscous shock waves for Boltzmann equation in Eulerian coordinate without the zero initial mass condition.

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