Electron. J. Diff. Eqns., Vol. 2003(2003), No. 63, pp. 1-15.

Weak solutions for a viscous p-Laplacian equation

Changchun Liu

Abstract:
In this paper, we consider the pseudo-parabolic equation $ u_t-k\Delta u_t=\mathop{\rm div}(|\nabla u|^{p-2}\nabla u)$. By using the time-discrete method, we establish the existence of weak solutions, and also discuss the uniqueness.

Submitted August 5, 2002. Published June 10, 2003.
Math Subject Classifications:
Key Words: Pseudo-parabolic equations, existence, uniqueness.

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Changchun Liu
Department of Mathematics, Nanjing Normal University
Nanjing 210097, China
Department of Mathematics, Jilin University
Changchun 130012, China
email: mathlcc@21cn.com

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