具有对流项的非线性奇摄动抛物型方程的周期解

Periodic Solutions to Singularly Perturbated Parabolic Nonlinear Equations with a Convection Term

本文证明了如果f和F关于t为周期函数,下面的奇摄动方程的边值问题有周期解: μ~2u_■=μ_t+bu_■+au+μF(x,t,u)+f(x,t)。文中亦给出解的渐近展式。

This paper proves that under some boundary conditions the followingequations μ~2u_(xx)=u_t+bu_x+au+μF (x, t, u) +f(x, t)have a periodic solution if f and F are periodic in t. The asymptotic expansion forthe solution is also given,