中文摘要：

当拟线性双曲系统线性退化时，其Cauchy问题最左族和最右族行波解是稳定的．而其中间族行波解未必稳定．我们在弱线性退化条件下，证明了拟线性双曲系统Cauchy问题适当小的W1,1 ∩L∞范数适当小的行波解是稳定的，并将此稳定性应用于可对角化的拟线性双曲系统和Chaplygin气体动力学方程组．

英文摘要：

Under linearly degenerate condition, the stability of leftmost and right- most families of traveling wave solutions to Cauchy problem for quasilinear hyperbolic system had been established in our recent work, while for the intermediate families, their possible instability is illustrated. This paper is concerned with the stability of traveling wave solutions with appropriate small W1,1 ∩L∞ norm to Cauchy problem for quasilinear hyperbolic system under weakly linearly degenerate condition, and the stability results can be applied to the diagonalizable quasilinear hyperbolic systems and Chaplygin gas.