非线性奇摄动问题的广义内部冲击层解

摘要

研究了一类广义奇摄动反应扩散方程初始边值问题。在适当的假设下，考虑了退化问题的广义解，然后利用广义函数理论构造了原问题的冲击层和边界层渐近解。再利用不动点定理证明了具有广义内部冲击层的渐近解的一致有效性。%A class of singular perturbation problem of the reaction diffusion initial value equation was studied .Under suitable conditions ,the generalized outer solution to reduced problems was considered . Then the interior shock and boundary layer correction solutions to the original problem were constructed by using the theory of generalized functions .Finally ,using the fixed point theorem ,the uniform validity of the generalized asymptotic solution with interior shock and initial layers was proved .