Global solutions via partial information and the Cahn-Hilliard equation

Jan Cholewa; Tomasz Dłotko

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 39-50
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Cholewa, Jan, and Dłotko, Tomasz. "Global solutions via partial information and the Cahn-Hilliard equation." Banach Center Publications 33.1 (1996): 39-50. <http://eudml.org/doc/262869>.

@article{Cholewa1996,
abstract = {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.},
author = {Cholewa, Jan, Dłotko, Tomasz},
journal = {Banach Center Publications},
keywords = {a priori estimates; Cahn-Hilliard equation; global existence; compact semigroups; higher order parabolic equations; global solutions; semilinear parabolic equations},
language = {eng},
number = {1},
pages = {39-50},
title = {Global solutions via partial information and the Cahn-Hilliard equation},
url = {http://eudml.org/doc/262869},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Cholewa, Jan
AU - Dłotko, Tomasz
TI - Global solutions via partial information and the Cahn-Hilliard equation
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 39
EP - 50
AB - 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.
LA - eng
KW - a priori estimates; Cahn-Hilliard equation; global existence; compact semigroups; higher order parabolic equations; global solutions; semilinear parabolic equations
UR - http://eudml.org/doc/262869
ER -

References

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  2. [2] H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc. 293 (1986), 191-227. Zbl0635.47056
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  4. [4] J. W. Cholewa, Classical Peano approach to quasilinear parabolic equations of arbitrary order, submitted. 
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  13. [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. [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. Zbl0592.35013
  15. [15] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Springer, Berlin, 1984. Zbl0546.35003
  16. [16] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1983. Zbl0508.35002
  17. [17] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988. Zbl0662.35001
  18. [18] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag Wiss., Berlin, 1978; also: North-Holland, Amsterdam, 1978. Zbl0387.46033
  19. [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. 

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