拟线性双曲型方程组Cauchy问题行波解的稳定性  

Stability of Traveling Wave Solutions to Cauchy Problem for Quasilinear Hyperbolic Systems

作　　者：薛晓琳[1] 刘存明[1] 

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《数学学报（中文版）》2016年第6期745-760,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金青年资助项目(11401421)

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W^(1,1)∩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.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.

关 键 词：拟线性双曲系统 初值问题 行波解 弱线性退化 

分 类 号：O175.27[理学—数学]