ABSTRACT
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.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Zhixiong Zhang http://orcid.org/0000-0003-3886-3701