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Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing

  • * Corresponding author: Mogtaba Mohammed

    * Corresponding author: Mogtaba Mohammed 

Dedicated to the memory of Professor Salah-Eldin A. Mohammed (May 20, 1946 - Dec 21, 2016)

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  • In this paper we deal with the homogenization of stochastic nonlinear hyperbolic equations with periodically oscillating coefficients involving nonlinear damping and forcing driven by a multi-dimensional Wiener process. Using the two-scale convergence method and crucial probabilistic compactness results due to Prokhorov and Skorokhod, we show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a nonlinear damped stochastic hyperbolic partial differential equation. More importantly, we also prove the convergence of the associated energies and establish a crucial corrector result.

    Mathematics Subject Classification: Primary: 60H15, 80M35, 80M40; Secondary: 35L70.

    Citation:

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