Asymptotic Solutions Of Some Singularly Perturbed Third Order Equations With Discontinuities At The Right End

In this paper,two kinds of singularly perturbed third-order problems with discon-tinuities at the right end are studied.The boundary layer function method and the space contrast theory are used to sew the inner layer functions.The corresponding formal asymptotic solutions are obtained,and the remainder is estimated to verify the exis-tence of the solutions.The first chapter mainly introduces the development history of singularly perturbed theory and the singularly perturbed theory methods proposed by researchers,and briefly describes the theorems needed in this paper,and introduces the origin of the right end discontinuity problem.In the second chapter,the mixed boundary value problem for a class of singularly perturbed third-order equations without y is studied.The formal asymptotic solutions with boundary layer and inner layer are constructed by using the boundary layer func-tion method.The continuity and smoothness of the solutions for the inner layer are guaranteed by the undetermined method and the stitching method in the space contrast theory,At the same time,a simple method is used to calculate the remainder.In the third chapter,based on the results of the second chapter,we further study the mixed boundary value problem for a class of singularly perturbed third-order equations with y-discontinuities.We construct and solve the formal asymptotic solution of the problem.By using the corresponding Nagumo theorem in the literature,we prove the existence of the solution and estimate the remainder,The images of the asymptotic and numerical solutions are compared to verify the corresponding results.The fourth chapter makes a comprehensive summary of this paper,and points out the research areas and prospects.