Abstract
In this paper we study the existence, uniqueness and the asymptotic behavior of the solution of a one dimensional linear thermoelastic system. Such a system is composed of a wave equation coupled with the heat equation and, physically, model the interaction of the vibrations of an elastic string with the variation of its temperature. We prove, first, the existence and uniqueness of solution of the system making use of the Theory of Semigroups of Bounded Linear Operators. For the analysis of the asymptotic behavior of the solution, we use a method consisting of a suitably perturbation to the energy of the system and, with that, we prove that the total energy of the system decays exponentially to zero as t → ∞.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
