一类消失项带有时间导数的对流方程  

A New Class Of Convection Equation With Vanishing Terms Containing Time Derivative

作　　者：王乐乐[1] 林京[2] 

机构地区：[1]同济大学数学系,上海200092 [2]合肥工业大学理学院,合肥230009

出　　处：《应用数学学报》2007年第6期1018-1029,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(NO.10671144);国家基础研究发展计划子课题(2007CB814903)部分资助项目.

摘　　要：本文在Duijn等的基础上研究了方程ht+f(h)x=εhxx+ε2τ1hxxt+ε2τhxxx的行波解,其中f(h)∈C2(R)是满足所谓凹凸性的任意已知函数,得出了在不同的τ1,τ2条件下,该方程行波解的存在性条件和唯一性条件,并利用行波解得到上述方程的解,从而得到了对流方程的弱解,并分析了对流方程的多解性.In this paper, we study the following equation： ht＋f（h）x=εhxx＋ε^2τ1hxxt＋ε^2τhxxx, where f（h）∈C2（R） is a smooth function satisfying the convex-concave condition. If ho is fixed, then we get the existence and uniqueness of the solution of the above equation under some conditions on T1, T2. Also we can obtain the weak solution of the corresponding convection equation by vanishing viscosity method and we discuss the non-uniqueness of the weak solution of the convection equation.

关 键 词：对流方程 行波解 古典激波 非古典激波 

分 类 号：O175.29[理学—数学]