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Pré-Publication, Document De Travail Année : 2020

ASYMPTOTIC DECOMPOSITION OF SOLUTIONS TO RANDOM PARABOLIC OPERATORS WITH OSCILLATING COEFFICIENTS

Résumé

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case the homogenized operator is deterministic. We obtain the leading terms of the asymptotic expansion of the solution , these terms being deterministic functions, and show that a properly renormalized difference between the solution and the said leading terms converges to a solution of some SPDE.
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Dates et versions

hal-02954085 , version 1 (30-09-2020)

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Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier. ASYMPTOTIC DECOMPOSITION OF SOLUTIONS TO RANDOM PARABOLIC OPERATORS WITH OSCILLATING COEFFICIENTS. 2020. ⟨hal-02954085⟩
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