Abstract parabolic problem with non-Lipschitz nonlinearity

Jan Cholewa; Tomasz Dlotko

Banach Center Publications (2000)

  • Volume: 52, Issue: 1, page 73-81
  • ISSN: 0137-6934

Abstract

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An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.

How to cite

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Cholewa, Jan, and Dlotko, Tomasz. "Abstract parabolic problem with non-Lipschitz nonlinearity." Banach Center Publications 52.1 (2000): 73-81. <http://eudml.org/doc/209064>.

@article{Cholewa2000,
abstract = {An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.},
author = {Cholewa, Jan, Dlotko, Tomasz},
journal = {Banach Center Publications},
keywords = {dissipative semigroup; parabolic system; Cauchy problem; global attractor; global solution; continuous nonlinearity},
language = {eng},
number = {1},
pages = {73-81},
title = {Abstract parabolic problem with non-Lipschitz nonlinearity},
url = {http://eudml.org/doc/209064},
volume = {52},
year = {2000},
}

TY - JOUR
AU - Cholewa, Jan
AU - Dlotko, Tomasz
TI - Abstract parabolic problem with non-Lipschitz nonlinearity
JO - Banach Center Publications
PY - 2000
VL - 52
IS - 1
SP - 73
EP - 81
AB - An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
LA - eng
KW - dissipative semigroup; parabolic system; Cauchy problem; global attractor; global solution; continuous nonlinearity
UR - http://eudml.org/doc/209064
ER -

References

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  1. [C-C-D] A. N. de Carvalho, J. W. Cholewa and T. Dlotko, Examples of global attractors in parabolic problems, Hokkaido Math. J. 27 (1998), 77-103. Zbl0898.35013
  2. [C-D] J. W. Cholewa and T. Dlotko, Global attractor for sectorial evolutionary equation, J. Differential Equations 125 (1996), 27-39. Zbl0853.34048
  3. [DL] T. Dlotko, Parabolic equation modelling diffusion with strong absorption, Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 61-70. Zbl0707.35071
  4. [FR] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. 
  5. [HA] J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, R. I., 1988. Zbl0642.58013
  6. [HE] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin, 1981. 
  7. [LA] O. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Cambridge University Press, Cambridge, 1991. Zbl0755.47049
  8. [L-M] J. H. Lightbourne and R. H. Martin, Relatively continuous nonlinear perturbations of analytic semigroups, Nonlinear Analysis TMA 1 (1977), 277-292. Zbl0356.34073
  9. [MA] R. H. Martin, Invariant sets and a mathematical model involving semilinear differential equations, in: Nonlinear Equations in Abstract Spaces, Proc. Inter. Symp. Univ. of Texas Arlington, Academic Press, New York 1978, 135-148. 
  10. [PA 1] A. Pazy, A class of semi-linear equations of evolution, Israel J. Math. 20 (1975), 23-36. Zbl0305.47022
  11. [PA 2] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983. 

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