二阶非线性奇摄动方程的激波解

Shock solution to nonlinear singularly perturbed equation of second-order

考虑了一个二阶非线性奇摄动方程的Dirichlet问题.利用微分不等式理论证明了该问题解的存在性,并指出了解的上下界,还利用匹配法求得了该问题的激波解,并给出了该问题的激波解、激波位置与边值的关系.

A Dirichlet problem of nonlinear singularly perturbed equation of the second-order was considered. With the theory of differential inequalities, the existence of solution to the problem was proved, and the upper and lower bounds of the solution were pointed out. Then with the matching method, the shock solution to the problem and the relation between the shock positions and boundary values were obtained.