一类一维的辐射流体力学方程组激波的存在性

Abstract

Abstract:

In this paper, the authors mainly study shock waves in a one-dimensional radiation hydrodynamic system. By using the Rankine-Hugoniot condition and entropy condition, this problem can be formulated as an initial boundary value problem with a free boundary for radiation hydrodynamic system. First, the authors transform this free boundary to the fixed one by using change of variables involving unknowns. Then they investigate the existence and uniqueness of the solution to the initial boundary value problem for this nonlinear system. For this problem, the authors first construct an approximate solution by using the compatibility conditions of the data. Then they use the Picard iteration and the Newton iteration for this nonlinear system respectively to construct a sequence of approximate solutions. By using a series of estimates and a compactness argument, the convergence of the sequence of approximate solutions is obtained. The limit of
this sequence gives a shock wave of the original radiation hydrodynamic system.

Key words: One-dimensional radiation hydrodynamic systems, Shock waves, Existence

CLC Number:

78A40

ZHU Yi-Feng, JIANG Peng. Existence of a Shock Wave in a One-dimensional Radiation Hydrodynamic System[J].Acta mathematica scientia,Series A, 2011, 31(1): 1-17.

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Existence of a Shock Wave in a One-dimensional Radiation Hydrodynamic System

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