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Curved squeezing of unbounded domains and attractors

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Abstract

In this paper, we prove attractor existence and continuation results for reaction–diffusion equations on singularly perturbed unbounded curved squeezed domains.

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References

  1. Antoci F., Prizzi M.: Reaction-diffusion equations on unbounded thin domains. Topol. Methods Nonlinear Anal. 18, 283–302 (2001)

    MATH  MathSciNet  Google Scholar 

  2. Carbinatto M C., Rybakowski K.P.: Resolvent convergence for Laplace operators on unbounded curved squeezed domains. Topol. Methods Nonlinear Anal. 42, 233–256 (2013)

    MathSciNet  Google Scholar 

  3. J. W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems. Cambridge University Press, Cambridge, 2000.

  4. J. K. Hale, Asymptotic Behavior of Dissipative Systems. Math. Surveys Monogr. 25, AMS, Providence, RI, 1988.

  5. Hale J.K., Raugel G.: Reaction-diffusion equations on thin domains. J. Math. Pures Appl. 9(71), 33–95 (1992)

    MathSciNet  Google Scholar 

  6. D. Henry, Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. 840, Springer, New York, 1981.

  7. O. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations. Cambridge University Press, Cambridge, 1991.

  8. M. Prizzi, On admissibility for parabolic equations in \({\mathbb{R}^n}\). Fund. Math. 176 (2003), 261–275.

  9. M. Prizzi, M. Rinaldi and K. P. Rybakowski, Curved thin domains and parabolic equations. Studia Math. 151 (2002), 109–140.

  10. Prizzi M., Rybakowski K.P.: Some recent results on thin domain problems. Topol. Methods Nonlinear Anal. 14, 239–255 (1999)

    MATH  MathSciNet  Google Scholar 

  11. M. Prizzi and K. P. Rybakowski, The effect of domain squeezing upon the dynamics of reaction-diffusion equations. J. Differential Equations 173 (2001), 271–320.

  12. M. Prizzi and K. P. Rybakowski, Attractors for reaction-diffusion equations on arbitrary unbounded domains. Topol. Methods Nonlinear Anal. 30 (2007), 251–277.

  13. K. P. Rybakowski, On curved squeezing and Conley index. Topol. Methods Nonlinear Anal. 38 (2011), 207–231.

  14. K. P. Rybakowski, Curved squeezing of unbounded domains and tail estimates. Topol. Methods Nonlinear Anal., to appear.

  15. Wang B.: Attractors for reaction-diffusion equations in unbounded domains. Phys. D 128, 41–52 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Krzysztof P. Rybakowski.

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To Professor Andrzej Granas

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Rybakowski, K.P. Curved squeezing of unbounded domains and attractors. J. Fixed Point Theory Appl. 16, 83–107 (2014). https://doi.org/10.1007/s11784-014-0205-0

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  • DOI: https://doi.org/10.1007/s11784-014-0205-0

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