PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2006 | 4 | 1 | 163-182
Tytuł artykułu

Finite dimensional global attractor for a class of doubly nonlinear parabolic equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
163-182
Opis fizyczny
Daty
wydano
2006-03-01
online
2006-03-01
Twórcy
Bibliografia
  • [1] H.W. Alt and S. Luckhaus: “Quasilinear elliptic-parabolic differential equations”, Math. Z., Vol. 183, (1983), pp. 311–341. http://dx.doi.org/10.1007/BF01176474
  • [2] T. Arai: “On the existence of the solution for ∂ϕ(u′(t)) + ∂ψ(u(t)) ∋ f(t)”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., Vol. 26, (1979), pp. 75–96.
  • [3] A.V. Babin and M.I. Vishik: Attractors of evolution equations, North-Holland, Amsterdam, 1992.
  • [4] A. Bamberger: “Etude d'une équation doublement non linéaire”, J. Funct. Anal., Vol. 24, (1977), pp. 148–155. http://dx.doi.org/10.1016/0022-1236(77)90051-9
  • [5] V. Barbu: Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leiden, 1976.
  • [6] H. Brezis: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973.
  • [7] P. Colli: “On some doubly nonlinear evolution equations in Banach spaces”, Japan J. Indust. Appl. Math., Vol. 9, (1992), pp. 181–203. http://dx.doi.org/10.1007/BF03167565
  • [8] P. Colli and A. Visintin: “On a class of doubly nonlinear evolution problems”, Comm. Partial Diff. Eqns., Vol. 15, (1990), pp. 737–756.
  • [9] E. DiBenedetto and R.E. Showalter: “Implicit degenerate evolution equations and applications”, S.I.A.M. J. Math. Anal., Vol. 12, (1981), pp. 731–751. http://dx.doi.org/10.1137/0512062
  • [10] A. Eden, C. Foias, B. Nicolaenko and R. Temam: Exponential attractors for dissipative evolution equations, Research in Applied Mathematics, Vol. 37, John-Wiley, New York, 1994.
  • [11] A. Eden, B. Michaux and J.-M. Rakotoson: “Doubly nonlinear parabolic-type equations as dynamical systems”, J. Dyn. Diff. Eqns., Vol. 3, (1991), pp. 87–131. http://dx.doi.org/10.1007/BF01049490
  • [12] A. Eden and J.-M. Rakotoson: “Exponential attractors for a doubly nonlinear equation”, J. Math. Anal. Appl., Vol. 185(2), (1994), pp. 321–339. http://dx.doi.org/10.1006/jmaa.1994.1251
  • [13] M. Efendiev, A. Miranville and S. Zelik: “Exponential attractors for a nonlinear reaction-diffusion system in R 3”, C. R. Acad. Sci. Paris Sér. I, Vol. 330, (2000), pp. 713–718.
  • [14] C.M. Elliott and R. Schätzle: “The limit of the anisotropic double-obstacle Allen-Cahn equation”, Proc. Royal Soc. Edin. A, Vol. 126, (1996), pp. 1217–1234.
  • [15] O. Grange and F. Mignot: “Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires”, J. Funct. Anal., Vol. 11, (1972), pp. 77–92. http://dx.doi.org/10.1016/0022-1236(72)90080-8
  • [16] M. Gurtin: “Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance”, Physica D, Vol. 92, (1996), pp. 178–192. http://dx.doi.org/10.1016/0167-2789(95)00173-5
  • [17] O.A. Ladyzhenskaya and N.N. Ural'ceva: Equations aux dérivées partielles de type elliptique, Monographies universitaires de Mathématiques, Vol. 31, Dunod, 1968.
  • [18] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
  • [19] J. Malek and D. Prazak: “Long time behavior via the method of l-trajectories”, J. Diff. Eqns., Vol. 18(2), (2002), pp. 243–279. http://dx.doi.org/10.1006/jdeq.2001.4087
  • [20] D. Prazak: “A necessary and sufficient condition for the existence of an exponential attractor”, Cent. Eur. J. Math., Vol. 1(3), (2003), pp. 411–417.
  • [21] P.-A. Raviart: “Sur la résolution de certaines équations paraboliques non linéaires”, J. Funct. Anal., Vol. 5, (1970), pp. 299–328. http://dx.doi.org/10.1016/0022-1236(70)90031-5
  • [22] A. Segatti: “Global attractor for a class of doubly nonlinear abstract evolution equations”, Discrete Cont. Dyn. Systems, To appear.
  • [23] K. Shirakawa: “Large time behavior for doubly nonlinear systems generated by sub-differentials”, Adv. Math. Sci. Appl., Vol. 10, (2000), pp. 77–92.
  • [24] R.E. Showalter: Monotone operators in Banach spaces and nonlinear partial differential equations, Amer. Math. Soc., Providence, R.I., 1997.
  • [25] J. Simon: “Régularité de la solution d'un problème aux limites non linéaire”, Ann. Fac. Sci. Toulouse, Vol. 3(3–4), (1981), pp. 247–274.
  • [26] J.E. Taylor and J.W. Cahn: “Linking anisotropic sharp and diffuse surface motion laws via gradient flows”, J. Statist. Phys., Vol. 77(1–2), (1993), pp. 183–197.
  • [27] R. Temam: Infinite dimensional dynamical systems in mechanics and physics, 2nd ed., Springer-Verlag, 1997.
  • [28] A. Visintin: Models of phase transitions, Birkhäuser, Boston, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1007_s11533-005-0010-5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.