Author:
Marin Marin,Vlase Sorin,Neagu Denisa
Abstract
AbstractOur 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.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference34 articles.
1. Kaltenbacher, B., Lasiecka, I., Marchand, R.: Wellposedness and exponential decay rates for the Moore–Gibson–Thompson equation arising in high intensity ultrasound. Control Cybern. 40(40), 971–988 (2011)
2. Lasiecka, I., Wang, X.: Moore–Gibson–Thompson equation with memory, part II: general decay of energy. J. Differ. Equ. 259(259), 7610–7635 (2015)
3. Dell’Oro, F., Pata, V.: On the Moore–Gibson–Thompson equation and its relation to linear viscoelasticity. Appl. Math. Optim. 76, 641–655 (2017)
4. Conti, M., Pata, V., Quintanilla, R.: Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature. Asymptot. Anal. 120(1–2), 1–21 (2020)
5. Pellicer, M., Sola-Morales, J.: Optimal scalar products in the Moore–Gibson–Thompson equation. Evol. Equ. Control Theory 8, 203–220 (2019)