摘要
We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(∞, t) = u + and u_– 【 u_+, where the correspondingCauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, becauseof the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signsof the characteristic speeds f(u_±) of boundary state u_– = u(0) and the far fields states u_+ =u(∞). In all cases both global existence of the solution and asymptotic behavior are shown underthe smallness conditions.
We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(∞, t) = u + and u_– < u_+, where the correspondingCauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, becauseof the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signsof the characteristic speeds f(u_±) of boundary state u_– = u(0) and the far fields states u_+ =u(∞). In all cases both global existence of the solution and asymptotic behavior are shown underthe smallness conditions.
基金
Supported by the National Natural Science Foundation of China (No.10171037, No. 10401012)
