Well-Posedness Of The Generalized Burgers Equation On A Finite Interval

In this paper, we study the initial-boundary value problem of the generalized Burgers equation posed on a finite interval with non-homogeneous boundary conditions. The boundary conditions are given in a general form, which covers the usual Dirichlet, Neumann or Robin boundary conditions. For the generalized Burgers equation, we establish the local well-posedness for the weak solution in when the Sobolev index is negative. Besides, for the classical Burgers equation with Dirichlet boundary conditions, we obtain the global well-posedness.