Exponential stability for a class of linearhyperbolic equations with hereditary memory

Monica Conti; Elsa M. Marchini; Vittorino Pata

doi:10.3934/dcdsb.2013.18.1555

Article Contents

2013, Volume 18, Issue 6: 1555-1565. Doi: 10.3934/dcdsb.2013.18.1555

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Exponential stability for a class of linear hyperbolic equations with hereditary memory

1.
Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano
2.
Politecnico di Milano - Dipartimento di Matematica “F. Brioschi”, Via Bonardi 9, 20133 Milano

Received: June 2011

Revised: November 2011

Published: August 2013

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Abstract

We establish a necessary and sufficient condition of exponential stability for the contraction semigroup generated by an abstract version of the linear differential equation $$∂_t u(t)-\int_0^\infty k(s)\Delta u(t-s)ds = 0 $$ modeling hereditary heat conduction of Gurtin-Pipkin type.

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Mathematics Subject Classification: 35B40, 45K05, 45M10, 47D03.

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