带一般边界和大初始扰动条件的广义BBM-Burgers方程解的渐近性态

摘要

This paper is concerned with the initial-boundary value problem for the generalized BBM-Burgers equation ut +f(u)x =uxx+uxxt with the general boundary condition u(0,t) -u_(t)→u_ (t→ ∞ ) , u_(t) -u_ ≤0 and the initial date satisfing u(x,0) = u0(x)→ u+(X→∞ ) , u_ (0) = uo(O) and u_ <00,f'(0) =f(0) =0. we prove that the global solution exists and converges time-asymptotically to the superposition of a strong stationary wave and a strong rarefaction wave for the large initial-boundary disturbance by using of the L2 - energy method.%研究广义BBM-Burgers方程ut+f(u)x=uxx+uxxtt的一般初边值问题,其边界满足u(0,t)=u_(t)→u_(t→∞),u_(t)-u_≤0；初始值满足u(x,0)=u0(x)→u+(x→∞),u_(0)=u0(0)且u_＜0＜u+.在流函数f满足f″(u) ＞0,f′(0)=f(0)=0以及初边值为大扰动的条件下,用L2-能量方法证明其解的整体存在性及渐近收敛于强稳定波和强稀疏波的叠加.