On a composite obtained by a mixture of a dipolar solid with a Moore–Gibson–Thompson media

• Published in: Boundary value problems 2024-01, Vol.2024 (1), p.16-9, Article 16
• Main Authors: Marin, Marin, Vlase, Sorin, Neagu, Denisa
• Format: Article
• Language: English
• Subjects: Analysis; Approximations and Expansions; Boundary value problems; Difference and Functional Equations; Dipolar bodies; Elastic media; Euclidean space; Hilbert space; Initial conditions; Instability; Kinematics; Lagrange identities; Linear operators; Mathematics; Mathematics and Statistics; Mixtures; Moore–Gibson–Thompson theory; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; Uniqueness; Viscoelasticity
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-024-01823-9

Our study is dedicated to a mixture composed of a dipolar elastic medium and a viscous Moore–Gibson–Thompson (MGT) material. The mixed problem with initial and boundary data, considered in this context, is approached from the perspective of the existence of a solution to this problem as well as the uniqueness of the solution. Considering that the mixed problem is very complex, both from the point of view of the basic equations and that of the initial conditions and the boundary data, the classical methods become difficult. That is why we preferred to transform it into a problem of Cauchy type on a conveniently constructed Hilbert space. In this way, we immediately proved both the existence and uniqueness of the solution, with techniques from the theory of semigroups of linear operators.