Uniform general stability of a coupled Volterra integro-differential equations with fading memories

In this work, we consider a coupled linear integro-differential wave system with memory. We study the existence and uniqueness of global solutions and prove the uniform stabilization of the total energy when time goes to infinity. To do this, we follow the lines of Conti et al. (Math Models Methods...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-04, Vol.74 (2), Article 66
Main Authors: Buriol, C., Delatorre, L. G., Tavares, E. H. Gomes, Soares, D. C.
Format: Article
Language:English
Subjects:
Differential equations
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Volterra integral equations
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Summary:In this work, we consider a coupled linear integro-differential wave system with memory. We study the existence and uniqueness of global solutions and prove the uniform stabilization of the total energy when time goes to infinity. To do this, we follow the lines of Conti et al. (Math Models Methods Appl Sci 18(1):21–45, 2008) and Conti and Pata (Z Angew Math Phys 71(1):6, 2020) and use the semigroup approach as the main tool.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-023-01963-5