PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1996 | 33 | 1 | 39-50
Tytuł artykułu

Global solutions via partial information and the Cahn-Hilliard equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Global solutions of semilinear parabolic equations are studied in the case when some weak a priori estimate for solutions of the problem under consideration is already known. The focus is on the rapid growth of the nonlinear term for which existence of the semigroup and certain dynamic properties of the considered system can be justified. Examples including the famous Cahn-Hilliard equation are finally discussed.
Rocznik
Tom
33
Numer
1
Strony
39-50
Opis fizyczny
Daty
wydano
1996
Twórcy
  • Institute of Mathematics, Silesian University, 40-007 Katowice, Poland
  • Institute of Mathematics, Silesian University, 40-007 Katowice, Poland
Bibliografia
  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
  • [2] H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc. 293 (1986), 191-227.
  • [3] J. W. Bebernes and K. Smitt, On the existence of maximal and minimal solutions for parabolic partial differential equations, Proc. Amer. Math. Soc. 73 (1979), 211-218.
  • [4] J. W. Cholewa, Classical Peano approach to quasilinear parabolic equations of arbitrary order, submitted.
  • [5] J. W. Cholewa and T. Dłotko, Global attractor for the Cahn-Hilliard system, Bull. Austral. Math. Soc. 49 (1994), 277-293.
  • [6] T. Dłotko, Fourth order semilinear parabolic equations, Tsukuba J. Math. 16 (1992), 389-405.
  • [7] T. Dłotko, Global attractor for the Cahn-Hilliard equation in $H^2$ and $H^3$, J. Differential Equations 113 (1994), 381-393.
  • [8] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
  • [9] J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, R.I., 1988.
  • [10] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, Berlin, 1981.
  • [11] W. Mlak, Hilbert Spaces and Operator Theory, Kluwer Academic Publishers and PWN, Dordrecht-Warszawa, 1991.
  • [12] J. L. Lions et E. Magenes, Problèmes aux Limites non Homogènes et Applications, Vol. I, Dunod, Paris, 1968.
  • [13] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, R.I., 1968.
  • [14] B. Nicolaenko, B. Scheurer and R. Temam, Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors, Physica 16D (1985), 155-183.
  • [15] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Springer, Berlin, 1984.
  • [16] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1983.
  • [17] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.
  • [18] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag Wiss., Berlin, 1978; also: North-Holland, Amsterdam, 1978.
  • [19] W. von Wahl, Global solutions to evolution equations of parabolic type, in: Differential Equations in Banach Spaces, Proceedings, 1985, A. Favini and E. Obrecht (eds.), Springer, Berlin, 1986, 254-266.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv33z1p39bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.