On porous‐elastic system with a time‐varying delay term in the internal feedbacks. Issue 8 (7th June 2020)

• Record Type: Journal Article
• Authors: Borges Filho, E.; Santos, M. L.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 100:Issue 8(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-06-07
• Subjects: exponential decay -- global solutions -- time‐varying delay; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800247
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In this article, we consider the one‐dimensional equations of an homogeneous and isotropic porous‐elastic solid with interior time‐dependent delay term feedbacks. First, using the variable norm technique of T. Kato, we prove that the system is well‐posed under some hypothesis adopted. Then, via a suitable Lyapunov functional, we show that the system is exponentially stable. Abstract : In this article, we consider the one‐dimensional equations of an homogeneous and isotropic porous‐elastic solid with interior time‐dependent delay term feedbacks. First, using the variable norm technique of T. Kato, we prove that the system is well‐posed under some hypothesis adopted. Then, via a suitable Lyapunov functional, we show that the system is exponentially stable.