一类两参数非线性反应扩散方程奇摄动问题的广义解

Abstract

A class of generalized singularly perturbed problems of reaction diffusion equations with two parameters were considered with the singular perturbation method. Firstly, under suitable conditions, the outer solution to the problem was found. Next, the power series of the two small parameters were developed, and the first and second boundary layer corrective terms for the solution to the problem were constructed with the multiscale variable method, respectively. Finally, based on the composite expansion method, the asymptotic expression of the generalized solution to the problem was obtained, and according to the fixed point theory for functional analysis, the precision of the asymptotic expansion was estimated. Two corrective functions with different thicknesses were obtained for the generalized solution in the overlapping area, and they take effects on the boundary conditions respectively and expand the range of study; moreover, the work provides a costruction method for this kind of corrective terms with different thicknesses in the overlapping area, thus has a wide study foreground.