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Pullback Attractors of Stochastic Lattice Dynamical Systems with a Multiplicative Noise and Non-Lipschitz Nonlinearities

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Book cover Differential and Difference Equations with Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

Abstract

In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions. Using the theory of multivalued random dynamical systems we prove the existence of a pullback compact global attractor.

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References

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Acknowledgements

This work has been partially supported by Ministerio de Ciencia e Innovación (Spain) MTM2008-00088, and Junta de Andalucía P07-FQM-02468 and FEDER.

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Authors and Affiliations

  1. Depto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain

    Tomás Caraballo

  2. Departament d’Economia Aplicada, Universitat de València, Campus dels Tarongers s/n, 46022, València, Spain

    Francisco Morillas

  3. Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202, Elche, Spain

    José Valero

Authors
  1. Tomás Caraballo
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  2. Francisco Morillas
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  3. José Valero
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Corresponding author

Correspondence to Tomás Caraballo .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Caraballo, T., Morillas, F., Valero, J. (2013). Pullback Attractors of Stochastic Lattice Dynamical Systems with a Multiplicative Noise and Non-Lipschitz Nonlinearities. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_27

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