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On porous‐elastic system with a time‐varying delay term in the internal feedbacks
Author(s) -
Borges Filho E.,
Santos M. L.
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800247
Subject(s) - term (time) , isotropy , homogeneous , norm (philosophy) , porous medium , mathematical analysis , mathematics , porosity , physics , geology , geotechnical engineering , combinatorics , quantum mechanics , political science , law
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.