<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>classical</italic> 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.</p></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.

On weak regularity requirements of the relaxation modulus in viscoelasticity

Dipartimento di Scienze di Base e Applicate per l’Ingegneria

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On weak regularity requirements of the relaxation modulus in viscoelasticity"}

The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in viscoelasticity is here considered. The...

On weak regularity requirements of the relaxation modulus in viscoelasticity

Published Online: May 11, 2019

Page range: 78 - 87

Received: Nov 16, 2018

Accepted: Apr 24, 2019

DOI: https://doi.org/10.2478/caim-2019-0014

Keywords
Materials with memory, Viscoelasticity, hyperbolic integro-differential problem, Regular kernel integro-differential systems, Singular kernel integro-differential systems

© 2019 Sandra Carillo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On weak regularity requirements of the relaxation modulus in viscoelasticity

Published Online: May 11, 2019

Page range: 78 - 87

Received: Nov 16, 2018

Accepted: Apr 24, 2019

DOI: https://doi.org/10.2478/caim-2019-0014

KeywordsMaterials with memory, Viscoelasticity, hyperbolic integro-differential problem, Regular kernel integro-differential systems, Singular kernel integro-differential systems

© 2019 Sandra Carillo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Materials with memory, Viscoelasticity, hyperbolic integro-differential problem, Regular kernel integro-differential systems, Singular kernel integro-differential systems