Electron. J. Diff. Eqns., Vol. 2006(2006), No. 70, pp. 1-18.

Weak solutions for quasilinear degenerate parabolic systems

Zheng'an Yao, Wenshu Zhou

This paper concerns the initial Dirichlet boundary-value problem for a class of quasilinear degenerate parabolic systems. Due to the degeneracies, the problem does not have classical solutions in general. Combining the special form of the system, a proper concept of a weak solution is presented, then the existence and uniqueness of weak solutions are proved. Moreover, the asymptotic behavior of weak solutions will also be discussed.

Submitted December 12, 2005. Published July 7, 2006.
Math Subject Classifications: 35K10, 35K50, 35K55, 35K65.
Key Words: Quasilinear degenerate parabolic system; weak solution; existence; uniqueness; asymptotic behavior.

Show me the PDF file (258K), TEX file, and other files for this article.

Zheng'an Yao
Department of Mathematics
Sun Yat-sen University
Guangzhou 510275, China
email: mcsyao@mail.sysu.edu.cn
Wenshu Zhou
Department of Mathematics
Jilin University
Changchun 130012, China
email: wolfzws@163.com

Return to the EJDE web page