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arXiv · 1811.06723

On weak regularity requirements of the relaxation modulus in viscoelasticity

Sandra Carillo·Michel Chipot·Vanda Valente·Giorgio Vergara Caffarelli
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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.

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Sandra Carillo, Michel Chipot, Vanda Valente, Giorgio Vergara Caffarelli. 2018-11-16. On weak regularity requirements of the relaxation modulus in viscoelasticity. https://doi.org/10.2478/caim-2019-0014

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