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Stability for the damped wave equation with neutral delay
Author(s) -
Tatar Nassereddine
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600229
Subject(s) - mathematics , infinity , viscoelasticity , stability (learning theory) , wave equation , damped wave , mathematical analysis , exponential stability , physics , computer science , nonlinear system , thermodynamics , quantum mechanics , machine learning
Of concern is a wave equation with a distributed neutral delay. We prove that, despite the destructive nature of delays in general, solutions may go back to the equilibrium state in an exponential manner as time goes to infinity. Reasonable conditions on the distributed neutral delay are established. This type of problems appear in the study of wave propagation in viscoelastic media and in acoustic wave propagation. It is not well studied so far.