Asymptotic method for parabolic partial differential equation with periodical boundary value condition

Parabolic partial differential equation with periodical boundary value condition is considered. The equation also contains small parameter in x direction and different small parameter in t direction. The present of small parameter leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The solution changes rapidly near three boundary layer. Left boundary layer function, right boundary layer function and bottom boundary layer function are derived by introducing three stretched variable and comparing small parameter in equation. The asymptotic solution is approximated by the degenerate solution and three boundary layer functions. Finally, numerical result is also presented in support of the proposed method.