PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2007 | 5 | 4 | 720-732
Tytuł artykułu

Decay rates of Volterra equations on ℝN

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This note is concerned with the linear Volterra equation of hyperbolic type $$\partial _{tt} u(t) - \alpha \Delta u(t) + \int_0^t {\mu (s)\Delta u(t - s)} ds = 0$$ on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
4
Strony
720-732
Opis fizyczny
Daty
wydano
2007-12-01
online
2007-12-01
Twórcy
autor
Bibliografia
  • [1] M. Conti, S. Gatti, V. Pata: “Uniform decay properties of linear Volterra integrodifferential equations”, Math. Models Methods Appl. Sci. (to appear).
  • [2] C.M. Dafermos: “An abstract Volterra equation with applications to linear viscoelasticity”, J. Differential Equations, Vol. 7, (1970), pp. 554–569. http://dx.doi.org/10.1016/0022-0396(70)90101-4
  • [3] C.M. Dafermos: “Asymptotic stability in viscoelasticity”, Arch. Rational Mech. Anal., Vol. 37, (1970), pp. 297–308. http://dx.doi.org/10.1007/BF00251609
  • [4] C.M. Dafermos: “Contraction semigroups and trend to equilibrium in continuum mechanics”, in Applications of Methods of Functional Analysis to Problems in Mechanics, P. Germain and B. Nayroles Eds.), Lecture Notes in Mathematics no.503, Springer-Verlag, Berlin-New York, 1976, pp.295–306 http://dx.doi.org/10.1007/BFb0088765
  • [5] G. Dassios, F. Zafiropoulos: “Equipartition of energy in linearized 3-D viscoelasticity”, Quart. Appl. Math., Vol. 48, (1990), pp. 715–730.
  • [6] M. Fabrizio, B. Lazzari: “On the existence and asymptotic stability of solutions for linear viscoelastic solids”, Arch. Rational Mech. Anal., Vol. 116, (1991), pp. 139–152. http://dx.doi.org/10.1007/BF00375589
  • [7] M. Fabrizio, A. Morro, “Mathematical problems in linear viscoelasticity”, SIAM Studies in Applied Mathematics no.12, SIAM Philadelphia, 1992.
  • [8] M. Grasselli, V. Pata: “Uniform attractors of nonautonomous systems with memory”, in Evolution Equations, Semigroups and Functional Analysis, A. Lorenzi and B. Ruf (Eds.), Progr. Nonlinear Differential Equations Appl. no.50, Birkhäuser Boston, 2002, pp.155–178.
  • [9] Z. Liu, S. Zheng: “On the exponential stability of linear viscoelasticity and thermoviscoelasticity”, Quart. Appl. Math., Vol. 54, (1996), pp. 21–31.
  • [10] J.E. Muñoz Rivera: “Asymptotic behaviour in linear viscoelasticity”, Quart. Appl. Math., Vol. 52, (1994), pp. 629–648.
  • [11] J.E. Muñoz Rivera, E. Cabanillas Lapa: “Decay rates of solutions of an anisotropic inhomogeneous n-dimensional viscoelastic equation with polynomially decaying kernels”, Comm. Math. Phys., Vol. 177, (1996), pp. 583–602. http://dx.doi.org/10.1007/BF02099539
  • [12] V. Pata: “Exponential stability in linear viscoelasticity”, Quart. Appl. Math., Vol. 64, (2006), pp. 499–513.
  • [13] V. Pata, A. Zucchi: “Attractors for a damped hyperbolic equation with linear memory”, Adv. Math. Sci. Appl., Vol. 11, (2001), pp. 505–529.
  • [14] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
  • [15] M. Renardy, W.J. Hrusa, J.A. Nohel, Mathematical problems in viscoelasticity, John Wiley & Sons, Inc., New York, 1987.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0024-2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.