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Analysis, Probability, Applications, and Computation pp 221–229Cite as

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Exponential Mixing and Ergodic Theorems for a Damped Nonlinear Wave Equation with Space-Time Localised Noise

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Abstract

This paper is devoted to study a damped nonlinear wave equation driven by a space-time localised noise, in a bounded domain with a smooth boundary. The equation is supplemented with the Dirichlet boundary conditions. It is assumed that the random perturbation is non-degenerate. We prove that the Markov process generated by the solution possesses a unique stationary distribution which is exponentially mixing. A strong law of large numbers and the central limit theorem are derived for this Markov process and used to estimate the corresponding rates of convergence.

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References

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Author information

Authors and Affiliations

  1. Northern Borders University, College of Sciences, Arar, Kingdom of Saudi Arabia

    Ridha Selmi

  2. Mathematics Department, Faculty of Sciences, University of Tunis El Manar, Tunis, Tunisia

    Rim Nasfi

Authors
  1. Ridha Selmi
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  2. Rim Nasfi
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Corresponding author

Correspondence to Ridha Selmi .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Karl‐Olof Lindahl

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  3. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

  5. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Patrik Wahlberg

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Selmi, R., Nasfi, R. (2019). Exponential Mixing and Ergodic Theorems for a Damped Nonlinear Wave Equation with Space-Time Localised Noise. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_21

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