Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields
Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.
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Abstract
We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods.
Publishing Year
Date Published
2023-09-01
Journal Title
Stochastics and Partial Differential Equations: Analysis and Computations
Publisher
Springer Nature
Acknowledgement
I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.
Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
11
Page
1254–1378
ISSN
IST-REx-ID
Cite this
Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w
Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w
Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-022-00254-w.
N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.
Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.
Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w.
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