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Singular limit of dissipative hyperbolic equations with memory

Pages: 200 - 208, Issue Special, August 2005

 Abstract        Full Text (210.6K)              

Monica Conti - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)
Vittorino Pata - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)
M. Squassina - Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy (email)

Abstract: We consider a class of weakly damped semilinear hyperbolic equations with memory, expressed by a convolution integral. We study the passage to the singular limit when the memory kernel collapses into the Dirac mass at zero, and we establish a convergence result for a proper family of exponential attractors.

Keywords:  Hyperbolic equations with memory, singular limit, exponential attractors.
Mathematics Subject Classification:  35B25, 35L05, 37L30, 45K05.

Received: June 2004;      Revised: March 2005;      Published: September 2005.