Variational formulation for fractional hyperbolic problems in the theory of viscoelasticity

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 73; no. 5
• Main Authors: Bravo-Castillero, Julián, López Ríos, Luis Fernando
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-10-2022; Springer Nature B.V
• Subjects: Engineering; Galerkin method; Mathematical Methods in Physics; Theoretical and Applied Mechanics; Viscoelasticity; 74D05; 35A15; 35R11; Galerkin method; Fractional partial differential equations; 65M12; Viscoelastic media
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-022-01826-5

In this article, a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary viscoelasticity is studied. An appropriate functional setting is introduced in order to establish the existence, uniqueness and a priori estimates for weak solutions. This framework is developed in close concordance with important physical quantities of the theory of viscoelasticity.