Two-Point Boundary Values For Burgers Equation And Generlized Burgers Equation

In this paper, two-point boundary values problems of the Burgers equation and the generalized Burgers equation are studied, where f(u) is smooth function and In the sec-ond section, we find the formal solution to the Burgers equation in the region 00, and then we prove that the solution is what we are searching for t > 0. To the generalized Burgers equation, we discuss it in the rest several sections. In the third section, the asymptotic behaviors of the solution for the generalized Burgers equation with convective function and nonconvective function are analyzed, respectively, both of which tend to the corresponding steady equation. In the forth section, the blowup of the solution is discussed to the initial-boundary value problem with sufficient large initial value in the region 0 < x < L.