一类高阶非线性奇异扰动非局部稳态系统Robin问题

On a Class of High-Order Nonlinear Singular Perturbed Nonlocal Systems’Steady State Robin Problem

讨论了一类高阶非线性积分-微分奇异扰动系统稳态Robin问题.首先,建立了高阶非线性非局部微分系统解的微分不等式理论.然后,构造了问题的外部解,并利用局部坐标系求得了边界层校正项,从而得到了解的形式渐近表示式.最后,利用微分不等式理论,证明了解的渐近表示式的一致有效性.

A class of high-order nonlinear integral-differential singular perturbation systems’steady state Robin problem was discussed.Firstly,the theory of differential inequality for the high-order nonlinear nonlocal differential system was built.Then,the outer solution to the problem was structured and the boundary layer corrective term was obtained by means of the local coordinate system.Thus the formal asymptotic expansion of the solution was got.Finally,the uniform validity of the asymptotic expansion of the solution was proved with the theory of differential inequality.