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Well posedness and asymptotic behavior of a wave equation with distributed time‐delay and Neumann boundary conditions
Author(s) -
Chentouf Boumediène,
Guesmia Aissa
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5682
Subject(s) - mathematics , resolvent , exponential stability , mathematical analysis , neumann boundary condition , term (time) , wave equation , boundary (topology) , von neumann architecture , damped wave , displacement (psychology) , work (physics) , nonlinear system , pure mathematics , mechanical engineering , engineering , psychology , physics , quantum mechanics , psychotherapist
This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems.