𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Polynomial stability without polynomial decay of the relaxation function

✍ Scribed by Nasser-eddine Tatar

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
115 KB
Volume
31
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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 Β© 2008 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

On the Stability of Some Exponential Pol
On the Stability of Some Exponential Polynomials
✍ Margarete Baptistini; PlΓ‘cido TΓ‘boas πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 195 KB

This paper studies elementary transcendental equations of the type z q pz q . z n q e q rz s 0, where p, q, r g ‫,ޒ‬ , p ) 0, q G 0, r / 0, n s 0, 1, 2. We are mainly interested in the case n s 0 for which a characterization of stability is accomplished; that is, we state a necessary and sufficient

On the Convergence of Polynomial Approxi
On the Convergence of Polynomial Approximation of Rational Functions
✍ Guo-Jin Wang; Thomas W. Sederberg; Falai Chen πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 389 KB

This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r\_r

Some Families of Generating Functions fo
Some Families of Generating Functions for the Bessel Polynomials
✍ Sheldon Yang; H.M Srivastava πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 177 KB

The main object of this paper is to show how readily some general results on bilinear, bilateral, or mixed multilateral generating functions for the Bessel polyno-Ε½ . mials would provide unifications and generalizations of numerous generating functions which were proven recently by using group-theor

On the preservation of stability in fami
On the preservation of stability in families of polynomials via substitutions
✍ Guillermo FernΓ‘ndez-Anaya; JosΓ© Alvarez-RamΓ­rez πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 128 KB

In this work, we use the Hadamard representation of polynomials and several known results on the stability of polynomial families to describe new polynomial families which are stable under substitutions. Such polynomial families can be seen as nonlinear stable perturbations of &small-in-parameters'

Tau-Function Constructions of the Recurr
Tau-Function Constructions of the Recurrence Coefficients of Orthogonal Polynomials
✍ Yang Chen; Mourad E.H Ismail; Walter Van Assche πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 283 KB

In this paper we compute the recurrence coefficients of orthogonal polynomials using -function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potenti