{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T00:32:01Z","timestamp":1773189121520,"version":"3.50.1"},"reference-count":133,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100005156","name":"Alexander von Humboldt-Stiftung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"crossref"}]},{"name":"CNRS"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2025,12,31]]},"DOI":"10.1137\/24m1689697","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T09:00:58Z","timestamp":1760518858000},"page":"1607-1664","source":"Crossref","is-referenced-by-count":3,"title":["Steklov\u2013Neumann Spectral Problem: Asymptotic Analysis and Applications to Diffusion-Controlled Reactions"],"prefix":"10.1137","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6273-9164","authenticated-orcid":true,"given":"Denis S.","family":"Grebenkov","sequence":"first","affiliation":[{"name":"Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e (UMR 7643), CNRS \u2013 Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France, and CNRS - Universit\u00e9 de Montr\u00e9al CRM - CNRS, 6128 succ Centre-Ville, Montr\u00e9al QC H3C 3J7, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1039\/qr9662000421"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1679757"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.pc.34.100183.002425"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bb.14.060185.001023"},{"key":"ref5","volume-title":"Diffusion-Limited Reactions","author":"Rice S.","year":"1985"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.3390\/molecules28227570"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511606014"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7687-0"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1142\/9104"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2014.02.003"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/120898395"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1142\/10578"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1142\/q0209"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-67802-8"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-46475-1"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1063\/1.5115030"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.062110"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.078102"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/abb6e4"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.032125"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/abc9a3"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac411a"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.054402"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ac85ec"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac6138"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.106.044121"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.034141"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac5e75"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2022.0615"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1063\/5.0146512"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.044105"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.014110"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/23M1545835"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.24033\/asens.516"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1090\/noti1073"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.4171\/JST\/164"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s13163-023-00480-3"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/237"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1081\/NFA-120039655"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.07.023"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-013-9215-3"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2015.1031383"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-016-9370-4"},{"key":"ref44","first-page":"225","volume-title":"Parallel Numerical Algorithms","author":"Smith B. F.","year":"1996"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210506001144"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2012-21038-y"},{"key":"ref47","first-page":"537","volume":"71","author":"Delitsyn A. L.","year":"2018","journal-title":"Quart J. Mech. Appl. Math."},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598333613"},{"key":"ref49","first-page":"65","volume":"25","author":"Calder\u00f3n A. P.","year":"1980","journal-title":"in Seminar on Numerical Analysis and Its Applications to Continuum Physics, Soc. Brasileira de Matem\u00e1tica, R\u00edo de Janeiro"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/18\/6\/201"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.2307\/1971291"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1137\/0151051"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/BF01627938"},{"key":"ref54","first-page":"703","volume":"23","author":"Troesch B. A.","year":"1972","journal-title":"J. Appl. Math. Phys."},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1007\/BF01596214"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1007\/BF00948809"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1002\/mma.442"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1112\/plms.12461"},{"key":"ref59","first-page":"19","volume":"231","author":"Ba\u00f1uelos R.","year":"2010","journal-title":"Amer. Math. Soc. Transl."},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004121000712"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109211"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1137\/0153038"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1063\/1.1475756"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-004-5712-8"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792505006145"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-005-8026-6"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-005-8027-5"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-005-8028-4"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0706599104"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.168105"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.051111"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1063\/1.3081633"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1137\/090752511"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1137\/100782620"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.02.025"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.021131"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0455-6"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.031105"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-014-1116-6"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.012137"},{"key":"ref81","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.260201"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-016-1653-2"},{"key":"ref83","doi-asserted-by":"publisher","DOI":"10.1039\/C6CP06102H"},{"key":"ref84","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ab5de4"},{"key":"ref85","first-page":"100047","volume":"5","author":"Kaye J.","year":"2020","journal-title":"J. Comput. Phys. X"},{"key":"ref86","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.034134"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375590"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad7fab"},{"key":"ref89","volume-title":"Strongly Elliptic Systems and Boundary Integral Equations","author":"McLean W. C. H.","year":"2000"},{"key":"ref90","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.07.012"},{"key":"ref91","volume-title":"Perturbation Theory for Linear Operators","author":"Kato T.","year":"1980","edition":"2"},{"key":"ref92","doi-asserted-by":"publisher","DOI":"10.1515\/9783110550887-004"},{"key":"ref93","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.021111"},{"key":"ref94","first-page":"021045","volume":"10","author":"Giuggioli L.","year":"2020","journal-title":"Phys. Rev. X"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aa8ed9"},{"key":"ref96","doi-asserted-by":"publisher","DOI":"10.1039\/C8CP02043D"},{"key":"ref97","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ac4282"},{"key":"ref98","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310158"},{"key":"ref99","first-page":"1","volume":"3","author":"Hitotumatu S.","year":"1954","journal-title":"Comment. Math. Univ. St. Paul."},{"key":"ref100","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2000.0690"},{"key":"ref101","doi-asserted-by":"publisher","DOI":"10.1007\/BF00281494"},{"key":"ref102","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.055306"},{"key":"ref103","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2022.09.003"},{"key":"ref104","doi-asserted-by":"publisher","DOI":"10.1007\/BF00282438"},{"key":"ref105","first-page":"49","volume":"21","author":"Simi\u0107 S.","year":"2006","journal-title":"Facta Univer. Ser. Math. Inform."},{"key":"ref106","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-009-9295-z"},{"key":"ref107","first-page":"2090","volume":"11","author":"Mandal M.","year":"2021","journal-title":"J. Appl. Anal. Comput."},{"key":"ref108","doi-asserted-by":"publisher","DOI":"10.1134\/S0012266122090099"},{"key":"ref109","doi-asserted-by":"publisher","DOI":"10.1070\/SM1992v071n01ABEH001394"},{"key":"ref110","doi-asserted-by":"publisher","DOI":"10.1063\/1.1605497"},{"key":"ref111","doi-asserted-by":"publisher","DOI":"10.1007\/s12220-021-00678-1"},{"key":"ref112","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8522(49)90023-9"},{"key":"ref113","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.73.3314"},{"key":"ref114","first-page":"135","volume-title":"Focus on Probability Theory","author":"Grebenkov D. S.","year":"2006"},{"key":"ref115","doi-asserted-by":"publisher","DOI":"10.1137\/060663258"},{"key":"ref117","doi-asserted-by":"publisher","DOI":"10.1063\/5.0128276"},{"key":"ref118","unstructured":"J. W. S. Baron Rayleigh, The Theory of Sound, Vol. 2, 2nd ed. Dover, New York, 1945."},{"key":"ref119","volume-title":"Diffusion Processes and Their Sample Paths","author":"Ito K.","year":"1965"},{"key":"ref120","series-title":"Ann. Math. Stud.","volume-title":"Functional Integrationand Partial Differential Equations","author":"Freidlin M.","year":"1985"},{"key":"ref121","doi-asserted-by":"publisher","DOI":"10.1007\/BF00699100"},{"key":"ref122","doi-asserted-by":"publisher","DOI":"10.1007\/BF01217746"},{"key":"ref123","doi-asserted-by":"publisher","DOI":"10.1112\/mtk.12134"},{"key":"ref124","unstructured":"M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965."},{"key":"ref125","volume-title":"Mixed Boundary Value Problems in Potential Theory","author":"Sneddon I. N.","year":"1966"},{"key":"ref126","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.041139"},{"key":"ref127","volume-title":"Laplace Transformations and Applications","author":"Watson E. J.","year":"1981"},{"key":"ref128","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2006.1796"},{"key":"ref129","volume-title":"Foundations of Potential Theory","author":"Kellogg O. D.","year":"1954"},{"key":"ref130","doi-asserted-by":"publisher","DOI":"10.1063\/1.5119969"},{"key":"ref131","doi-asserted-by":"publisher","DOI":"10.2140\/paa.2023.5.767"},{"key":"ref132","doi-asserted-by":"publisher","DOI":"10.1063\/5.0228529"},{"key":"ref133","doi-asserted-by":"publisher","DOI":"10.1007\/s11118-015-9473-6"},{"key":"ref134","doi-asserted-by":"publisher","DOI":"10.1063\/5.0278477"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T09:01:07Z","timestamp":1760518867000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1689697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,15]]},"references-count":133,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12,31]]}},"alternative-id":["10.1137\/24M1689697"],"URL":"https:\/\/doi.org\/10.1137\/24m1689697","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,15]]}}}