带一般边界BBM-Burgers方程强边界层解的稳定性

摘要

研究带一般边界条件的广义BBM - Burgers方程u.-utxx-uxx+f(u)x=0的初边值问题边界层解的非线性稳定性,其边界条件为u(t,0)=ub(t)→ub(t→+∞),初始值u(0,x)=u0(x)→u+(x→+∞)(u+≠yb).在f"(u)＞0,φ(x)＜0,f(ub)＜0的条件下,用L2-能量方法证明其强边界层解具有非线性稳定性,从而澄清一般边界条件对边界层解的稳定性的影响.%This paper is concerned with the nonlinear stability of boundary layer solution for general initial-boundary value problem for generalized BBM - Burgers equation ut - utxx-uxx+f(u)x =0 with tne general boundary condition u(t,0) = ub(t)→ub(t→+∞ ) and the initial data u(0,x) =u0(x)→u+(x→+∞) (u+≠ub). Under the condition that fn (u)> 0,φx (x ) < 0 and f' ( ub) < 0, the strong boundary layer solution for the above initial -boundary value problem has nonlinear stability by means of an L2 - energy method were proved. And clarified the effect of the general boundary data on the stability of boundary layer solution.