Exponential attractor for the delayed logistic equation with a nonlinear diffusion

Pages: 717 - 726, Issue Special, July 2003

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Dalibor Pražák - Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Prague 8, Czech Republic (email)

Abstract: We study the generalized logistic equation where the feedback is captured by the time convolution with a nonnegative measure and the diffusion is the laplacian plus the p-laplacian with $p >= 2$. We prove that the equation has an exponential attractor provided that the solutions are asymptotically bounded.

Keywords:  Exponential attractor, nonlinear dissipation, logistic equation, bounded delay.
Mathematics Subject Classification:  Primary: 37L25. Secondary: 37L30, 47J35.

Received: August 2002; Published: April 2003.