Numerical exponential decay of thermoelastic waves connected in parallel

• Published in: Advances in computational mathematics Vol. 49; no. 3
• Main Authors: Ramos, A. J. A., Campelo, A. D. S., Almeida Júnior, D. S., Freitas, M. M., Barbosa, R. C.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2023; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Discrete systems; Energy methods; Finite difference method; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Numerical methods; Parallel connected; Stabilization; Visualization; Wave equations; Numerical exponential decay; 35E15; 93D22; Finite-difference space; 65M06; Coupled thermoelastic wave
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-023-10027-1

In this paper, we study a system consisting of two wave equations connected in parallel and coupled to the heat diffusion equation. In the first moment, we present theoretical results on existence and uniqueness of solution and we prove the exponential stabilization of the associated semigroup. We analyze the semi-discrete problem in finite differences and we introduce for the first time in the literature the energy method to prove the exponential stabilization of the corresponding semi-discrete system. Finally, we present a fully discrete finite difference scheme that combines explicit and implicit integration methods and numerical simulations that illustrate the theoretical results.