Exponential attractors of reaction-diffusion systems in an unbounded domain
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We consider reaction-diffusion systems in unbounded domains, prove the existence of expotential attractors for such systems, and estimate their fractal dimension. The essential difference with the case of a bounded domain studied before is the continuity of the spectrum of the linear part of the equations. This difficulty is overcome by systematic use of weighted Sobolev spaces.
- A. V. Babin. Asymptotics as ¦x¦→ ∞ of a Strongly Perturbed Poisseuille Flow,Adv. Soviet Math. Vol. 10, AMS, Providence, RI, 1992.
- A. V. Babin and M. I. Vishik. Attractors of partial differential equations in an unbounded domain.Proc. Roy. Soc. Edinburgh 116A, 221–243, 1990.
- A. V. Babin and M. I. Vishik.Attractors of Evolution Equations, North Holland, Amsterdam, 1991.
- A. Babin and M. Vishik. Unstable invariant sets of semigroups of nonlinear oprators and their perturbations.Russ. Math. Surv. 41(4) (1986), 1–41.
- P. Constantin, C. Foias, B. Nicolaenko, and R. Teman.Integral and Inertial Manifolds for Dissipative Partial Differential Equations, Appl. Math. Sci. Vol. 70, Springer-Verlag, New York, 1989.
- A. Eden, C. Foias, B. Nicolaenko, and Z. S. She. Exponential attractors and their relevance to fluid mechanics systems.Physica D 63 (1993), 350–360.
- 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.
- C. Foias, G. Sell, and R. Temam. Inertial manifolds for nonlinear evolution equations.J. Diff. Eq. 73 (1988), 309–353.
- C. Foias and R. Temam. Some analytic and geometric properties of the solutions of the Navier-Stokes equations.J. Math. Pures Appl. 58 (1979), 339–368.
- J. Hale.Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, Vol. 25, AMS, Providence, RI, 1988.
- J. Hale, Lin, and G. Raugel, Lower semicontinuity of attractors of parabolic partial differential equations, preprint, Georgia Institute of Technology.
- T. Kato.Perturbation Theory for Linear Operators, Springer-Verlag, Berlin/New York, 1980.
- J. Mallet-Paret and G. Sell. Inertial manifolds for reaction-diffusion equations in higher space dimensions.J. Am. Math. Soc. 1 (1988), 805–866.
- R. Temam.Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, Vol. 68, Springer-Verlag, New York, 1988.
- Exponential attractors of reaction-diffusion systems in an unbounded domain
Journal of Dynamics and Differential Equations
Volume 7, Issue 4 , pp 567-590
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- Kluwer Academic Publishers-Plenum Publishers
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- Exponential attractors
- fractal dimension
- reaction-diffusion systems