Well-posedness of the generalized Burgers equation on a finite interval

ABSTRACT

In this paper, we study the initial-boundary value problem of the generalized Burgers equation posed on a finite interval $(0,L)$ 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 $H^s(0,L)$ when the Sobolev index is negative. Besides, for the classical Burgers equation with Dirichlet boundary conditions, we obtain the global well-posedness.

Keywords:

• Burgers equation
• initial-boundary value problem
• well-posedness

AMS CLASSIFICATIONS:

• 35A01
• 35C15
• 35D30
• 35K55
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zhixiong Zhang http://orcid.org/0000-0003-3886-3701

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant numbers 11301425, 11571244 and 11231007] and the PCSIRT of the Ministry of Education of China [grant number IRT_16R53].