Open AccessStability Result for a Weakly Nonlinearly Damped Porous System with Distributed Delay
Author(s) -
Khoudir Kibeche,
Lamine Bouzettouta,
Abdelhak Djebabla,
Fahima Hebhoub
Publication year - 2021
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-19-2021-812
Subject(s) - term (time) , nonlinear system , mathematics , regular polygon , stability (learning theory) , porous medium , multiplier (economics) , porosity , mathematical analysis , control theory (sociology) , computer science , physics , geometry , geotechnical engineering , control (management) , engineering , quantum mechanics , machine learning , artificial intelligence , economics , macroeconomics
In this paper, we consider a one-dimensional porous system damped with a single weakly nonlinear feedback and distributed delay term. Without imposing any restrictive growth assumption near the origin on the damping term, we establish an explicit and general decay rate, using a multiplier method and some properties of convex functions in case of the same speed of propagation in the two equations of the system. The result is new and opens more research areas into porous-elastic system.