Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel

Applied Mathematics and Computation

Volumn 167, Issue 2, 2005, Pages 1221-1235

  Medjden, Mohamed ^a   Tatar, Nasser Eddine ^b  

^a UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Exponential decay; Memory term; Relaxation function; Viscoelasticity

Indexed keywords

PROBLEM SOLVING;

EXPONENTIAL DECAY; KERNELS; MEMORY TERM; RELAXATION FUNCTION;

VISCOELASTICITY;

EID: 25144463982     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.08.035     Document Type: Article

References (16)

1. M.M. Cavalcanti, M. Aassila, and J.A. Soriano Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain SIAM J. Control Opt. 38 5 2000 1581 1602
2. H. Engler Weak solutions of a class of quasilinear hyperbolic integrodifferential equations describing viscoelastic materials Arch. Rat. Mech. Anal. 113 1991 1 38
3. M. Fabrizio, A. Morro, Mathematical Problems in Linear Viscoelasticity, SIAM Stud. Appl. Math., Philadelphia 1992.
4. K.B. Hannsgen, and R.L. Wheeler Behavior of the solutions of a Volterra equation as a parameter tends to infinity J. Integral Eqs. 7 1984 229 237
5. W.J. Hrusa Global existence and asymptotic stability for a nonlinear hyperbolic Volterra equation with large initial data SIAM J. Math. Anal. 16 1985 110 134
6. W.J. Hrusa, and M. Renardy On wave propagation in linear viscoelasticity Quart. Appl. Math. 43 1985 237 254
7. W.J. Hrusa, and M. Renardy On a class of quasilinear partial integrodifferential equations with singular kernels J. Diff. Eqs. 64 1986 195 220
8. W.J. Hrusa, and M. Renardy A model equation for viscoelasticity with a strongly singular kernel SIAM J. Math. Anal. 19 1988 257 269
9. S.O. Londen An existence result for a Volterra equation in a Banach space Trans. Am. Math. Soc. 235 1978 285 304
10. M. Medjden, N.-e. Tatar, On the wave equation with a temporal non-local term and a weak dissipation, submitted for publication.
11. J. Milota, J. Nečas, and V. Šverák On weak solutions to a viscoelasticity model Comment. Math. Univ. Carolinae 31 3 1990 557 565
12. J. Prüss Evolutionary Integral Equations and Applications 1993 Birkhaüser Verlag Basel
13. M. Renardy Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids Rheol. Acta 21 1982 251 254
14. M. Renardy Coercive estimates and existence of solutions for a model of one-dimensional viscoelasticity with a nonintegrable memory function J. Integral Eqs. Appl. 1 1988 7 16
15. M. Renardy, W.J. Hrusa, and J.A. Nohel Mathematical problems in viscoelasticity Pitman Monographs and Surveys in Pure and Applied Mathematics vol. 35 1987 John Wiley and Sons New York
16. Q. Tiehu Asymptotic behavior of a class of abstract integrodifferential equations and applications J. Math. Anal. Appl. 233 1999 130 147