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Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
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  • Published: February 2003

Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term

  • Sandra Cerrai1 

Probability Theory and Related Fields volume 125, pages 271–304 (2003)Cite this article

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Abstract

 We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains of ℝd, perturbed by a multiplicative noise. The reaction term is assumed to have polynomial growth and to be locally Lipschitz-continuous and monotone. The noise is white in space and time if d=1 and coloured in space if d>1; in any case the covariance operator is never assumed to be Hilbert-Schmidt. The multiplication term in front of the noise is assumed to be Lipschitz-continuous and no restrictions are given either on its linear growth or on its degenaracy. Our results apply, in particular, to systems of stochastic Ginzburg-Landau equations with multiplicative noise.

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Authors and Affiliations

  1. Dipartimento di Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, I-50134 Firenze, Italy. e-mail: s.cerrai@sns.it, , , , , , IT

    Sandra Cerrai

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  1. Sandra Cerrai
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Additional information

Received: 1 November 2001 / Revised version: 17 June 2002 / Published online: 14 November

Mathematics Subject Classification (2000): 60H15, 35R60, 47A35

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Cite this article

Cerrai, S. Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Probab Theory Relat Fields 125, 271–304 (2003). https://doi.org/10.1007/s00440-002-0230-6

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  • Issue Date: February 2003

  • DOI: https://doi.org/10.1007/s00440-002-0230-6

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Keywords

  • Colour
  • Covariance
  • Continuous Function
  • Multiplication Term
  • Invariant Measure
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