CAJ | 학술논문

本文研究了具有边界摄动的非线性时滞反应扩散方程奇摄动问题。首先得到了退化问题的解。其次构造了原问题的外部解。然后引入伸长变量构造了解的初始层校正项，得到了解的形式渐近展开式。最后在适当的假设下，利用微分不等式理论，证明了原初始边植问题解的渐近展开式的一致有效性。
본문연구료구유변계섭동적비선성시체반응확산방정기섭동문제。수선득도료퇴화문제적해。기차구조료원문제적외부해。연후인입신장변량구조료해적초시층교정항，득도료해적형식점근전개식。최후재괄당적가설하，이용미분불등식이론，증명료원초시변식문제해적점근전개식적일치유효성。
The nonlinear singular perturbation problem for the reaction diffusion time delay equation with boundary perturbation is considered in this paper. Firstly, the redu-ced solution is obtained. Secondly, the outer solution of the original problem is constructed. Then, introducing a stretched variable, the initial layer correction of solution is obtained. Finally, under the suitable conditions, applying the theory of differential inequalities the uniformly valid asymptotic expansion of solution for the original initial boundary value problem is proved.