一类右端不连续的奇异摄动拟线性Robin边值问题的内部层解

Solutions of Internal Layers for a Class of SingularlyPerturbed Quasilinear Robin Boundary Value Problemswith Discontinuous Right-Hand Side

考虑一类具有Robin边值条件的右端不连续的奇摄动拟线性微分方程.首先,在给定条件下构造在间断曲线附近具有内部层的光滑解的渐近表达式;其次,基于缝接法证明该问题解的存在性,并给出余项估计;最后,用数值算例验证该方法的有效性.

We consider a class of singularly perturbed quasilinear differential equation with Robin boundary value conditions and discontinuous right-hand side.Firstly,under the given conditions,the asymptotic expression of a smooth solution with an internal l ayer in the neighborhood of the discontinuous curve is constructed.Secondly,based on the matching technique,the existence of such solution is proved,and the remainder estimation is given.Finally,the effectiveness of the method is verified by a numerical example.