The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions

We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method.