保守场的一类特殊激波解  

A special class of shock wave of the conservation law

作　　者：王乐乐[1] 林京[1] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2007年第2期244-247,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：文章研究了一类消失项为εxxu+ε2τ1 xxtu+ε2τ2 xxxu时非凸保守场方程的激波解(弱解),通过构造行波的方法得到了近似方程行波解存在的必要条件,并讨论了该行波解的若干性质。证明了该行波解u(x,t,ε)的极限(ε→+0)就是保守场方程的弱解,并利用行波来构造该非凸保守场方程的激波解。This paper considers the shock waves of the non-convex conservation law when the vanishing term is εδxxμ＋ε^2τ1δxxtμ＋ε^2τ2δxxxμ By constructing the traveling wave, the necessary condition and some special properties are gained. It is proved that the limit of the traveling wave（ε→0） is the weak solution of the conservation law, then the shock wave o~ the conservation law can be obtained easily.

关 键 词：保守场 行波解 古典激波 非古典激波 

分 类 号：O175.22[理学—数学]