General decay of solutions of a viscoelastic equation

SA Messaoudi - Journal of Mathematical Analysis and Applications, 2008 - Elsevier
General decay of solutions of a viscoelastic equation Page 1 J. Math. Anal. Appl. 341 (2008)
1457–1467 www.elsevier.com/locate/jmaa General decay of solutions of a viscoelastic …

Optimal decay rates for the viscoelastic wave equation

MI Mustafa - Mathematical Methods in the Applied Sciences, 2018 - Wiley Online Library
In this paper, we consider a viscoelastic equation with minimal conditions on the relaxation
function g, namely,, where H is an increasing and convex function near the origin and ξ is a …

General stability result for viscoelastic wave equations

MI Mustafa, SA Messaoudi - Journal of Mathematical Physics, 2012 - pubs.aip.org
In this paper, we consider a viscoelastic equation and establish an explicit and general
decay rate result without imposing restrictive assumptions on the behavior of the relaxation …

Note on intrinsic decay rates for abstract wave equations with memory

I Lasiecka, SA Messaoudi, MI Mustafa - Journal of Mathematical …, 2013 - pubs.aip.org
In this paper we consider a viscoelastic abstract wave equation with memory kernel
satisfying the inequality g′+ H (g)⩽ 0, s⩾ 0 where H (s) is a given continuous, positive …

[HTML][HTML] General decay result for nonlinear viscoelastic equations

MI Mustafa - Journal of Mathematical Analysis and Applications, 2018 - Elsevier
In this paper we consider a nonlinear viscoelastic equation with minimal conditions on the L
1 (0,∞) relaxation function g namely g′(t)≤− ξ (t) H (g (t)), where H is an increasing and …

Well posedness and asymptotic behavior of a coupled system of nonlinear viscoelastic equations

MI Mustafa - Nonlinear Analysis: Real World Applications, 2012 - Elsevier
In this paper, we consider a nonlinear system of two coupled viscoelastic equations which
describes the interaction between two different fields arising in viscoelasticity. We prove the …

[HTML][HTML] A new approach to the stability of an abstract system in the presence of infinite history

A Guesmia, SA Messaoudi - Journal of Mathematical Analysis and …, 2014 - Elsevier
In this paper, we consider the following problem {utt (t)+ A u (t)−∫ 0+∞ g (s) A u (t− s) ds=
0,∀ t> 0 u (− t)= u 0 (t),∀ t⩾ 0 ut (0)= u 1, where A is a self-adjoint positive definite operator …

Arbitrary decays in linear viscoelasticity

N Tatar - Journal of mathematical physics, 2011 - pubs.aip.org
It is by now well known that a necessary condition for the exponential (polynomial) decay of
the energy of a problem arising in viscoelasticity is that the kernel (which appears in the …

General decay for a viscoelastic problem with not necessarily decreasing kernel

F Mesloub, S Boulaaras - Journal of Applied Mathematics and Computing, 2018 - Springer
In this paper, a problem which arises in viscoelasticity is considered. We obtain the decay
rate of the energy, for certain class of relaxation functions not necessarily exponentially or …

On convexity for energy decay rates of a viscoelastic equation with boundary feedback

SA Messaoudi, MI Mustafa - Nonlinear Analysis: Theory, Methods & …, 2010 - Elsevier
In this paper we consider a viscoelastic equation with a nonlinear feedback localized on a
part of the boundary. We establish an explicit and general decay rate result, using some …