The generalized Burgers equation with and without a time delay

[摘要] We consider the generalized Burgers equation with and without a time delay when the boundary conditions areperiodic with period2π. For the generalized Burgers equationwithout a time delay, that is,ut=vuxx−uux+u+h(x),00,u(0,t)=u(2π,t),u(x,0)=u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stability of theequation. As for the generalized time-delayed Burgers equation,that is,ut(x,t)=vuxx(x,t)−u(x,t−τ)ux(x,t)+u(x,t),00,u(0,t)=u(2π,t),t>0,u(x,s)=u0(x,s),0

[学科分类] 应用数学