Electron. J. Diff. Eqns., Vol. 2003(2003), No. 76, pp. 1-13.

Global attractors for a class of degenerate diffusion equations

Shingo Takeuchi & Tomomi Yokota

In this paper we give two existence results for a class of degenerate diffusion equations with p-Laplacian. One is on a unique global strong solution, and the other is on a global attractor. It is also shown that the global attractor coincides with the unstable set of the set of all stationary solutions. As a by-product, an a-priori estimate for solutions of the corresponding elliptic equations is obtained.

Submitted January 29, 2003. Revised May 8, 2003. Published July 11, 2003.
Math Subject Classifications: 35K65, 37L30.
Key Words: Global attractors, p-Laplacian, degenerate diffusion.

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Shingo Takeuchi
Department of General Education
Kogakuin University
2665-1 Nakano-machi
Hachioji-shi, Tokyo 192-0015, Japan
email: shingo@cc.kogakuin.ac.jp
Tomomi Yokota
Department of Mathematics
Tokyo University of Science
26 Wakamiya-cho
Shinjuku-ku, Tokyo 162-0827, Japan
email: yokota@rs.kagu.tus.ac.jp

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