中文摘要：

讨论了一类具有内层和初始层激波解的反应扩散方程初始边值问题．反应扩散方程的激波解，在核物理学、热力学，大气物理学，环境科学中有广泛的应用．本文首先引入伸长变量构造了问题解的内层和初始层．然后利用合成方法得到得到了解的形式渐近展开式．然后构造上、下解。最后利用微分不等式理论，证明了解的存在性和解的渐近展开式的一致有效性．

英文摘要：

In this paper, we consider a class of initial boundary value problem for the re- action diffusion equation, whose shock solution has the interior and initial layers. The shock solution of the reaction diffusion has wide applications in the nuclear physics, heat dynamics, atmospheric physics and environmental science. At first, we construct the interior and initial layers of solution. Then, we obtain the formal asymptotic expression of solution via the composed method. Next, we construct the super and lower solutions. Finally, by using the theory of differential inequalities, we prove the existence and uniform validity for the asymptotic expression of the solution.