Premium
Polynomial stability without polynomial decay of the relaxation function
Author(s) -
Tatar Nassereddine
Publication year - 2008
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.1018
Subject(s) - mathematics , polynomial , relaxation (psychology) , kernel (algebra) , function (biology) , stability (learning theory) , zero (linguistics) , stable polynomial , state (computer science) , work (physics) , polynomial kernel , exponential stability , mathematical analysis , matrix polynomial , combinatorics , square free polynomial , kernel method , thermodynamics , algorithm , physics , nonlinear system , quantum mechanics , computer science , philosophy , artificial intelligence , support vector machine , linguistics , biology , psychology , social psychology , evolutionary biology , machine learning
We consider a linear viscoelastic problem and prove polynomial asymptotic stability of the steady state. This work improves previous works where it is proved that polynomial decay of solutions to the equilibrium state occurs provided that the relaxation function itself is polynomially decaying to zero. In this paper we will not assume any decay rate of the relaxation function. In case the kernel has some flat zones then we prove polynomial decay of solutions provided that these flat zones are not too big . If the kernel is strictly decreasing then there is no need for this assumption. Copyright © 2008 John Wiley & Sons, Ltd.