Asymptotic Behaviors Of Solutions For The Initial-Boundary Value Problem Of Generalized BBM-Burgers Equation And Damped Wave Equation

This paper is concerned with the asymptotic behaviors of solutions for theinitial-boundary value problem of generalized BBM-Burgers equation and damped waveequation with the general boundary effect.For the generalized BBM-Burgers equation on the half space, under the condition thatthe flux function is convex and the initial perturbation is large, it is proved that the solution ofinitial-boundary value problem tends to the superposition of a strong stationary wave and astrong rarefaction wave by means ofL~2energy method and the corresponding convergencerate of solution is derived.For the damped wave equation on the bounded interval, under the condition that theconvex-flux function f satisfies the sub-characteristic|f’(u)|＜1and the initialperturbation is small, the asymptotic behavior of the solution of initial-boundary valueproblem is obtained by means ofL~2energy method. In the case of u_-＞u_+, the solutiontends to a strong stationary wave; in the case of u_-＞u_+, the solution tends to a weakstationary wave. Moreover, when u_±(t)≡u_±, and the corresponding exponential decay ratesare derived.