On weak regularity requirements of the relaxation modulus in viscoelasticity
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.
Keywords
Cite
@article{arxiv.1811.06723,
title = {On weak regularity requirements of the relaxation modulus in viscoelasticity},
author = {Sandra Carillo and Michel Chipot and Vanda Valente and Giorgio Vergara Caffarelli},
journal= {arXiv preprint arXiv:1811.06723},
year = {2019}
}