{"volume":11,"abstract":[{"lang":"eng","text":"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."}],"file_date_updated":"2023-08-14T11:51:04Z","date_created":"2021-10-23T10:50:22Z","publication_status":"published","language":[{"iso":"eng"}],"publication":"Stochastics and Partial Differential Equations: Analysis and Computations","_id":"10173","scopus_import":"1","oa":1,"file":[{"relation":"main_file","file_size":1635193,"date_created":"2023-08-14T11:51:04Z","checksum":"f83dcaecdbd3ace862c4ed97a20e8501","access_level":"open_access","file_id":"14052","file_name":"2023_StochPartialDiffEquations_Clozeau.pdf","creator":"dernst","success":1,"date_updated":"2023-08-14T11:51:04Z","content_type":"application/pdf"}],"day":"01","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","date_updated":"2023-08-14T11:51:47Z","external_id":{"arxiv":["2102.07452"],"isi":["000799715600001"]},"status":"public","author":[{"last_name":"Clozeau","first_name":"Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","full_name":"Clozeau, Nicolas"}],"acknowledgement":"I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","ddc":["510"],"doi":"10.1007/s40072-022-00254-w","type":"journal_article","article_type":"original","has_accepted_license":"1","page":"1254–1378","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        11","date_published":"2023-09-01T00:00:00Z","citation":{"chicago":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s40072-022-00254-w\">https://doi.org/10.1007/s40072-022-00254-w</a>.","ista":"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.","apa":"Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-022-00254-w\">https://doi.org/10.1007/s40072-022-00254-w</a>","short":"N. Clozeau, Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) 1254–1378.","mla":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:<a href=\"https://doi.org/10.1007/s40072-022-00254-w\">10.1007/s40072-022-00254-w</a>.","ama":"Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2023;11:1254–1378. doi:<a href=\"https://doi.org/10.1007/s40072-022-00254-w\">10.1007/s40072-022-00254-w</a>","ieee":"N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 11. Springer Nature, pp. 1254–1378, 2023."},"quality_controlled":"1","title":"Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields","publication_identifier":{"issn":["2194-0401"]},"month":"09","year":"2023"}