On weak regularity requirements of the relaxation modulus in viscoelasticity
- Carillo, Sandra I.N.F.N. - Sezione Roma1, Gr. IV - Mathematical Methods of NonLinear Physics (M.M.N.L.P.), Rome, Italy
- Chipot, Michel Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma La Sapienza, Via Antonio Scarpa 16, 00161 Rome, Italy
- Valente, Vanda Istituto per le Applicazioni del Calcolo M. Picone, Via dei Taurini 19, 00185 Roma, Italy
- Caffarelli, Giorgio Vergara Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma La Sapienza, Via Antonio Scarpa 16, 00161 Rome, Italy
Published in:
- Communications in Applied and Industrial Mathematics. - Walter de Gruyter GmbH. - 2019, vol. 10, no. 1, p. 78-87
English
Abstract
The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in viscoelasticity is here considered. The kernel, in the linear viscoelasticity equation, represents the relaxation function which is characteristic of the considered material. Specifically, the case of a kernel, which does not satisfy the classical regularity requirements is analysed. This choice is suggested by applications according to the literature to model a wider variety of materials. A notable example of kernel, not satisfying the classical regularity requirements, is represented by a wedge continuous function. Indeed, the linear integro-differential viscoelasticity equation, characterised by a suitable wedge continuous relaxation function, is shown to give the classical linear wave equation via a limit procedure.
- Language
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- English
- Open access status
- gold
- Identifiers
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- DOI 10.2478/caim-2019-0014
- ISSN 2038-0909
- Persistent URL
- https://sonar.ch/global/documents/151733
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