Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Exponential and polynomial decay for first order linear Volterra evolution equations

Authors: Edoardo Mainini and Gianluca Mola
Journal: Quart. Appl. Math. 67 (2009), 93-111
MSC (2000): Primary 35B41, 37L30, 45J05, 80A22
DOI: https://doi.org/10.1090/S0033-569X-09-01145-X
Published electronically: January 7, 2009
MathSciNet review: 2495073
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Abstract: We consider, in an abstract setting, an instance of the Coleman-Gurtin model for heat conduction with memory, that is, the Volterra integro-differential equation

$\displaystyle \partial_t u(t) - \beta \Delta u(t) - \int_{0}^{t}k(s)\Delta u(t-s)ds = 0. $

We establish new results for the exponential and polynomial decay of solutions, by means of conditions on the convolution kernel which are weaker than the classical differential inequalities.

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Additional Information

Edoardo Mainini
Affiliation: Classe di Scienze Scuola Normale Superiore Piazza dei Cavalieri 7, I-56126 Pisa, Italy
Email: edoardo.mainini@sns.it

Gianluca Mola
Affiliation: Dipartimento di Matematica “F.Brioschi” Politecnico di Milano Via Bonardi 9, I-20133 Milano, Italy & Department of Applied Physics, Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan
Email: gianluca.mola@polimi.it

DOI: https://doi.org/10.1090/S0033-569X-09-01145-X
Received by editor(s): July 9, 2007
Published electronically: January 7, 2009
Additional Notes: The second author was supported by the Postdoctoral Fellowship of the Japan Society for the Promotion of Sciences (No. PE06067).
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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