非线性积分-微分椭圆型方程边值问题激波解（英文）

The Shock Wave Solution to Boundary Value Problem for Nonlinear Integral-Differential Elliptic Equation

研究了一类非线性积分-微分椭圆型方程奇摄动边值问题.在适当的条件下,首先求出了原问题的外部解和内部激波层校正项;然后利用多重尺度变量和合成展开法构造出解的边界层项校正项;并得到解的形式渐近展开式;最后利用奇异摄动理论,研究了边值问题解的渐近展开式.并证明了原问题存在一个解和解的一致有效性.

The singularly perturbed boundary value problem for a class of nonlinear integral—differential elliptic equation is considered.Under suitable conditions,firstly,the outer solution and shock wave layer corrective term of the original problem is obtained.Secondly,using the multiple scales variable and the method of component expansion,the boundary layer corrective term is constructed and the formal asymptotic expansion is obtained.Finally,using the singular perturbation theory the asymptotic expansion of solution for the boundary value problem is studied.And the existence of solution to the original problem and the uniformly valid asymptotic estimation are proved.