Nonlinear Stability Of Boundary Layer Solutions For The General Initial-Boundary Value Problem Of Generalized Bbm-Burgers Equation

This paper is concerned with nonlinear stability of boundary layer solutions for thegeneralized BBM-Burgers equation with general boundary effect in the half space.For the generalied BBM-Burgers equation with general smooth nonlinear flux functionand general boundary effect and large initial perturbation, we prove that its weak non-monotone boundary layer solution has nonlinear stability by means of anL2energy method,and derive an algebraic and exponential convergence rates of solutions toward boundarylayer solutions to the above initial-boundary value problem by employing the space-timeweighted energy method.For the generalied BBM-Burgers equation with convex flux function and generalboundary effect and small initial perturbation, we prove that its strong decreasing boundarylayer solution has nonlinear stability by means of anL2energy method, and derive analgebraic and exponential convergence rates of solutions toward boundary layer solutions tothis initial-boundary value problem by employing the space-time weighted energy method.