The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in vis- coelasticity 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 contin- uous 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.
On weak regularity requirements of the relaxation modulus in viscoelasticity / Carillo, Sandra; Chipot, Michel; Valente, Vanda; Vergara-Caffarelli, Giorgio. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 10:1(2019), pp. 78-87. [10.2478/caim-2019-0014]
On weak regularity requirements of the relaxation modulus in viscoelasticity
Carillo, Sandra
Primo
;Vergara-Caffarelli, Giorgio
2019
Abstract
The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in vis- coelasticity 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 contin- uous 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.File | Dimensione | Formato | |
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