Long-time behavior of solutions of some doubly nonlinear equation

Abstract

The subject of this investigation is the qualitative properties of solutions of the equation

where nonlinear term g is supposed to satisfy the upper polynomial growth condition of arbitrary order and g′(s) > −l. The existence of a , -global attractor for this equation with Dirichlet boundary condition is proved.

Keywords:

• Nonlinear degenerate equation
• Compactness method
• Global attractor
• 2000 Mathematics Subject Classifications
• 35B41
• 35K55
• 35B65

Acknowledgement

The author would like to express his sincere thanks to the referee for valuable comments and suggestions.