The Transmission Problem of Viscoelastic Waves

Acta Applicandae Mathematicae

Volumn 62, Issue 1, 2000, Pages 1-

  Muñoz Rivera, Jaime E ^a   Oquendo, Higidio Portillo ^a  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Exponential decay; Materials with memory; Partially viscoelastic; Transmission problem

Indexed keywords

EID: 18344399455     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1006449032100     Document Type: Article

References (13)

1. Dafermos, C. M.: Asymptotic stability in viscoelasticity, Arch. Rat. Mech. Anal. 37 (1970), 297-308.
2. Dafermos, C. M.: An abstract Volterra equation with applications to linear viscoelasticity J. Differential Equations 1 (1970), 554-569.
3. Dassios, G. and Zafiropoulos, F.: Equipartition of energy in Linearized 3-D Viscoelasticity Quart. Appl. Math. 48(4) (1990), 715-730.
4. Dautray, R. and Lions, J. L.: Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Vol. 1, Masson, Paris, 1984.
5. Kawashima, S.: Global solutions to the equation of viscoelasticity with fading memory, J. Differentials Equations 101(2) (1993), 388-420.
6. Kim, J. U.: A boundary thin obstacle problem for a wave equation, Comm. Partial Differential Equations 14(8-9) (1989), 1011-1026. (1989).
7. Lagnese, J. E.: Boundary controllability in problems of transmission for a class of second order hyperbolics systems, ESAIM: Control, Optim. and Cal. Var. 2 (1997), 343-357.
8. Linz, P.: Analytical and Numerical Methods for Volterra Equations, Studies in Appl. Math. 7, SIAM, Philadelphia, 1985.
9. Lions, J. L.: Contrôlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués (tome 1), Collection RMA, Masson, Paris, 1988.
10. Liu, K. and Liu, Z.: Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping, SIAM J. Control Optim. 36 (1998), 1086-1098.
11. Muñoz Rivera, J. E.: Asymptotic behaviour in linear viscoelasticity, Quart. Appl. Math. III (4) (1994), 629-648.
12. Liu, Z. and Peng, C.: Exponential stability of a viscoelastic Timoshenko beam, Adv. Math. Sci. Appl. 8(1) (1998), 343-351.
13. Shen, G., Fulling, S. A., Narcowich, F. J. and Sun, S.: Exponential decay of energy of evolution equation with locally distributed damping, SIAM J. Appl. Math. 51(1) (1991), 266-301.