两参数非线性反应扩散积分微分方程的内层激波渐近解

Interior Shock Asymptotic Solutions to Nonlinear Reaction Diffusion Integral Differential Equations with Two Parameters

研究了一类两参数非线性反应扩散积分微分奇摄动问题.利用奇摄动方法,构造了问题的外部解、内部激波层、边界层及初始层校正项,由此得到了问题解的形式渐近展开式.最后利用积分微分方程的比较定理证明了该问题解的渐近展开式的一致有效性.

The singular perturbation problem for the nonlinear reaction diffusion integral differential problem with two parameters is considered. By using the singular perturbation method, the outer solution, interior shock layer, boundary layer and initial layer corrective terms are constructed, then the formal asymptotic expansion of solution is obtained. Finally, the uniform validity of asymptotic expansion for solution to this problem is proved by using the comparison theorem for integral differential equation.