{"id":"https://openalex.org/W7204199157","doi":"https://doi.org/10.5281/zenodo.22097338","title":"Ternary SteadyState Theory I: Capping Global WellPosedness for Delayed ReactionDiffusion Systems\u300a\u4e09\u5143\u7a33\u6001\u8bba I:\u65f6\u6ede\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u7684\u5168\u5c40\u9002\u5b9a\u6027\u5c01\u9876\u300b","display_name":"Ternary SteadyState Theory I: Capping Global WellPosedness for Delayed ReactionDiffusion Systems\u300a\u4e09\u5143\u7a33\u6001\u8bba I:\u65f6\u6ede\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u7684\u5168\u5c40\u9002\u5b9a\u6027\u5c01\u9876\u300b","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204199157","doi":"https://doi.org/10.5281/zenodo.22097338"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22097338","doi":"https://doi.org/10.5281/zenodo.22097338","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22097338","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22097338","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148109321","display_name":"Guojun Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang, Guojun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148109321"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.49219998717308044,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.49219998717308044,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.43309998512268066,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.04019999876618385,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/global-well-posedness","display_name":"global well-posedness","score":0.9990000128746033},{"id":"https://openalex.org/keywords/hadamard-well-posedness","display_name":"Hadamard well-posedness","score":0.9309999942779541},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7279999852180481},{"id":"https://openalex.org/keywords/continuous-dependence-on-initial-data","display_name":"continuous dependence on initial data","score":0.8389999866485596},{"id":"https://openalex.org/keywords/analytic-semigroups","display_name":"analytic semigroups","score":0.5720000267028809},{"id":"https://openalex.org/keywords/leray-schauder-fixed-point-theorem","display_name":"Leray-Schauder fixed point theorem","score":0.968999981880188},{"id":"https://openalex.org/keywords/hurwitz-stability-criterion","display_name":"Hurwitz stability criterion","score":0.8180000185966492},{"id":"https://openalex.org/keywords/hilbert-spaces","display_name":"Hilbert spaces","score":0.48100000619888306}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.7261999845504761},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6287000179290771},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6033999919891357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5968999862670898},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5917999744415283},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5047000050544739},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.43470001220703125},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.42739999294281006},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4106000065803528},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.3910999894142151},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3582000136375427},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.3474999964237213},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.34380000829696655},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C2778002589","wikidata":"https://www.wikidata.org/wiki/Q2406791","display_name":"Upset","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30979999899864197},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22097338","doi":"https://doi.org/10.5281/zenodo.22097338","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22097338","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22097339","doi":"https://doi.org/10.5281/zenodo.22097339","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22097339","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22097338","doi":"https://doi.org/10.5281/zenodo.22097338","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22097338","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"\u6587\u6863\u540d\u79f0:\u300a\u4e09\u5143\u7a33\u6001\u8bba":[0],"I:\u65f6\u6ede\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u7684\u5168\u5c40\u9002\u5b9a\u6027\u5c01\u9876\u300b":[1],"\u82f1\u6587\u6807\u9898:TSST":[2],"I:":[3,65],"Global":[4,50,67,439],"Well\u2011Posedness":[5,68],"of":[6,92,146,183,195,207,256,279,288,303,318,344,409,413],"a":[7,237,334,383],"Delayed":[8,70],"Reaction\u2011Diffusion":[9,71],"System":[10,87],"\u4f5c\u8005:\u6768\u56fd\u4fca,\u72ec\u7acb\u4ea4\u53c9\u5b66\u79d1\u7814\u7a76\u8005,\u4e2d\u56fd\u6606\u660e":[11],"\u5f00\u6e90\u8bb8\u53ef:CC":[12],"BY\u2011NC\u2011ND":[13,84],"4.0":[14,85],"International":[15,86],"\u4f53\u7cfb\u5f52\u5c5e:\u4e09\u5143\u7a33\u6001\u8bba(TSST)\u5916\u5ef6\u7279\u8f91\u7cfb\u5217,\u5f52\u6863\u7248\u672c":[16],"V30/V31/V32/V33\u3002\u672c\u6587\u4e0d\u4fee\u6539":[17],"V29":[18,22,35,272],"\u5df2\u6c38\u4e45\u51bb\u7ed3\u7684\u516c\u7406\u300111":[19],"\u7ef4\u5168\u57df\u72b6\u6001\u5411\u91cf\u3001\u4e3b\u63a7\u65b9\u7a0b\u3001\u7a33\u6001\u89e3\u7b49\u6838\u5fc3\u5bf9\u8c61,\u4ec5\u5f00\u5c55\u5916\u5ef6\u6570\u5b66\u63a8\u5bfc\u3002":[20],"\u5185\u5bb9\u6982\u8ff0":[21],"\u7248\u4e09\u5143\u7a33\u6001\u8bba\u642d\u5efa\u4e86\u52a8\u529b\u5b66\u6846\u67b6,\u7ed9\u51fa\u7a33\u6001\u4ee3\u6570\u7a33\u5b9a\u6027\u8bba\u8bc1\u4e0e\u53c2\u6570\u7a7a\u95f4\u7d27\u81f4\u6027\u7684\u76f4\u89c2\u63a8\u6f14,\u4f46\u5c1a\u5b58\u4e24\u5904\u6570\u5b66\u4e25\u8c28\u6027\u7f3a\u53e3:\u7b2c\u4e00,\u65f6\u6ede\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u89e3\u7684\u5b58\u5728\u6027\u3001\u552f\u4e00\u6027\u3001\u5bf9\u521d\u503c\u8fde\u7eed\u4f9d\u8d56\u6027(Hadamard":[23],"\u9002\u5b9a\u6027)\u7f3a\u5c11\u65e0\u7a77\u7ef4\u6cdb\u51fd\u5206\u6790\u6846\u67b6\u4e0b\u7684\u4e25\u683c\u8bc1\u660e;\u7b2c\u4e8c,\u5408\u6cd5\u53c2\u6570\u7a7a\u95f4\\(\\Theta_{valid}\\)\u7684\u7d27\u81f4\u6027\u4ec5\u4f9d\u9760\u76f4\u89c2\u8bba\u8ff0,\u5b58\u5728\u5faa\u73af\u8bba\u8bc1\u98ce\u9669,\u76f4\u63a5\u5173\u7cfb\u4e09\u5143\u667a\u80fd\u82af\u7247\u5de5\u7a0b\u4eff\u771f\u7684\u6570\u5b66\u53ef\u9760\u6027\u3002":[24],"\u672c\u6587\u5c06":[25],"TSST":[26,46,129,215,377,427],"\u4e3b\u63a7\u65b9\u7a0b\u91cd\u6784\u4e8e":[27],"Hilbert":[28,222],"\u7a7a\u95f4":[29],"\\(\\mathscr{H}=H^{1}(\\Omega;\\mathbb{R}^{11})":[30,224],"\\times":[31,225],"L^{2}([-\\tau,0];H^{1}(\\Omega;\\mathbb{R}^{11}))\\),\u514b\u670d\u539f\u8fde\u7eed\u51fd\u6570\u7a7a\u95f4\u4e2d\u6269\u6563\u7b97\u5b50\u65e0\u6cd5\u751f\u6210\\(C_0\\)\u2011\u534a\u7fa4\u7684\u7f3a\u9677\u3002\u501f\u52a9\u89e3\u6790\u534a\u7fa4\u7406\u8bba\u4e0e":[32],"Leray\u2011Schauder":[33,249],"\u4e0d\u52a8\u70b9\u5b9a\u7406\u8bc1\u660e\u89e3\u7684\u5c40\u90e8\u5b58\u5728\u552f\u4e00\u6027;\u6784\u9020\u4ee5":[34],"\u8d6b\u5c14\u7ef4\u8328\u7a33\u5b9a\u6027\u5224\u636e\u4e3a\u8f93\u5165\u7684\u65f6\u6ede":[36],"Lyapunov":[37,263],"\u6cdb\u51fd,\u5b9e\u73b0\u5c40\u90e8\u89e3\u5411\u5168\u90e8\u65f6\u95f4\u8f74\u7684\u5168\u5c40\u5ef6\u62d3,\u5e76\u8bc1\u660e\u89e3\u5bf9\u521d\u503c\u4e0e\u53c2\u6570\u7684\u8fde\u7eed\u4f9d\u8d56\u6027\u3002":[38],"\u4f9d\u6258\u5f97\u5230\u7684\u9002\u5b9a\u6027\u7ed3\u8bba,\u901a\u8fc7\u53cd\u8bc1\u6cd5\u8bc1\u660e\\(\\Theta_{valid}\\)\u7684\u6709\u754c\u6027;\u7ed3\u5408\u89e3\u5bf9\u53c2\u6570\u7684\u8fde\u7eed\u4f9d\u8d56\u6027\u4ee5\u53ca\u72b6\u6001\u7a7a\u95f4\u7684\u95ed\u6027\u8bc1\u660e\u95ed\u6027,\u5229\u7528\u6d77\u6d85\u2011\u535a\u96f7\u5c14\u5b9a\u7406\u4e25\u683c\u8bc1\u660e\\(\\Theta_{valid}\\)\u7d27\u81f4\u3002\u8fdb\u4e00\u6b65,\u8bc1\u660e\u5728\u5408\u6cd5\u53c2\u6570\u4e0e\u7269\u7406\u72b6\u6001\u7684\u4e58\u79ef\u7a7a\u95f4\u4e0a\u5b58\u5728\u6709\u9650\u7684\u7edf\u4e00\u5168\u5c40":[39],"Lipschitz":[40,338],"\u5e38\u6570,\u63a8\u5bfc\u663e\u5f0f\u6570\u503c\u79bb\u6563\u7a33\u5b9a\u6027\u6761\u4ef6,\u4e3a\u6709\u9650\u5143\u3001IMEX":[41],"\u7b49\u4eff\u771f\u683c\u5f0f\u7684\u6536\u655b\u5206\u6790\u4e0e\u8bef\u5dee\u4f30\u8ba1\u63d0\u4f9b\u652f\u6491\u3002":[42],"\u672c\u7814\u7a76\u5c06\u4e09\u5143\u7a33\u6001\u8bba\u4ece\u7269\u7406\u516c\u7406\u76f4\u89c9\u5347\u7ea7\u4e3a\u6cdb\u51fd\u5206\u6790\u6846\u67b6\u4e0b\u4e25\u683c\u9002\u5b9a\u7684\u52a8\u529b\u5b66\u4f53\u7cfb,\u4e3a\u4e09\u5143\u667a\u80fd\u82af\u7247\u3001\u8111\u673a\u63a5\u53e3\u786c\u4ef6\u3001\u5f00\u653e\u8017\u6563\u590d\u6742\u7cfb\u7edf\u4eff\u771f\u63d0\u4f9b\u65e0\u6761\u4ef6\u6536\u655b\u7684\u6570\u5b66\u7406\u8bba\u4f9d\u636e\u3002\u9644\u5f55\u5305\u542b":[43],"Sobolev":[44,410],"\u7a7a\u95f4\u5b9a\u4e49\u3001\u89e3\u6790\u534a\u7fa4\u7406\u8bba\u56de\u987e\u3001\u6570\u503c\u79bb\u6563\u7a33\u5b9a\u6027\u6761\u4ef6;\u6587\u672b\u9644\u5e26":[45],"\u5168\u7cfb\u5217\u5f52\u6863":[47],"DOI":[48,422],"\u6e05\u5355\u4e0e\u8457\u4f5c\u6743\u767b\u8bb0\u7d22\u5f15\u3002":[49],"Open\u2011Source":[51,440],"Guide":[52,441],"to":[53,235,275,360,382,442],"Ternary":[54,62,93,443],"Steady\u2011State":[55,63,94,444],"Theory":[56,64,95,445],"(TSST):":[57,446],"DOI:https://doi.org/10.5281/zenodo.22821646":[58,447],"English":[59],"Document":[60],"Title:":[61],"Capping":[66],"for":[69,138,144,168,203,331,355,367,395,425],"Systems":[72],"Author:":[73],"Guojun":[74],"Yang,":[75],"Independent":[76],"Interdisciplinary":[77],"Researcher,":[78],"Kunming,":[79],"China":[80],"Open\u2011access":[81],"License:":[82],"CC":[83],"Affiliation:":[88],"Extended":[89],"Special":[90],"Series":[91],"(TSST),":[96],"archive":[97,423],"version":[98],"V30/V31/V32V/33.":[99],"This":[100,374],"paper":[101],"performs":[102],"extended":[103],"mathematical":[104,154,201,393],"derivations":[105],"without":[106],"altering":[107],"any":[108],"permanently\u2011frozen":[109],"core":[110],"objects":[111],"from":[112,271,311,378],"V29,":[113],"including":[114],"axioms,":[115],"the":[116,132,147,169,184,214,221,228,231,240,248,267,283,319,323,327,341,426,437],"11\u2011dimensional":[117],"global":[118,277,337],"state":[119,321],"vector,":[120],"governing":[121,216],"dynamical":[122,133,386],"equations":[123],"and":[124,141,162,247,254,293,347,364,370,401,416],"steady\u2011state":[125,139],"solutions.":[126],"Abstract\u2011like":[127],"Description":[128],"Version\u201129":[130],"established":[131],"framework,":[134],"provided":[135],"algebraic":[136],"proof":[137],"stability":[140,269,353,418],"heuristic":[142,191],"reasoning":[143],"compactness":[145,182,329],"valid\u2011parameter":[148],"space.":[149,243],"Nevertheless,":[150],"two":[151],"gaps":[152],"in":[153],"rigor":[155],"remained.":[156],"First,":[157],"Hadamard":[158],"well\u2011posedness":[159,300],"(existence,":[160],"uniqueness":[161,255],"continuous":[163,286,312],"dependence":[164,287,313],"on":[165,220,314],"initial":[166,291],"data)":[167],"delayed":[170],"reaction\u2011diffusion":[171],"system":[172,294,387],"lacked":[173],"rigorous":[174,328],"justification":[175],"within":[176],"an":[177,391],"infinite\u2011dimensional":[178],"functional\u2011analytic":[179],"setting.":[180],"Second,":[181],"admissible":[185],"parameter":[186],"space":[187,223,343],"\\(\\Theta_{valid}\\)":[188,304],"rested":[189],"upon":[190,290,299],"arguments":[192],"with":[193,266,430],"risk":[194],"circular":[196],"reasoning,":[197],"which":[198],"directly":[199],"threatens":[200],"reliability":[202],"engineering\u2011oriented":[204],"numerical":[205,356,417],"simulation":[206,372],"ternary":[208,396],"intelligent":[209,397],"chips.":[210],"In":[211],"this":[212],"paper,":[213],"equation":[217],"is":[218,273,296,305,350],"reformulated":[219],"L^{2}([-\\tau,0];H^{1}(\\Omega;\\mathbb{R}^{11}))\\),":[226],"resolving":[227],"drawback":[229],"that":[230],"diffusion":[232],"operator":[233],"fails":[234],"generate":[236],"\\(C_0\\)\u2011semigroup":[238],"over":[239,340],"previous":[241],"continuous\u2011function":[242],"Applying":[244],"analytic\u2011semigroup":[245],"theory":[246],"fixed\u2011point":[250],"theorem,":[251],"local":[252,280],"existence":[253],"mild":[257],"solutions":[258,281,289],"are":[259,358,434],"proven.":[260,351],"A":[261,420],"delay\u2011dependent":[262],"functional":[264],"fed":[265],"Hurwitz":[268],"criterion":[270],"constructed":[274],"achieve":[276],"continuation":[278],"onto":[282],"full":[284,421],"time\u2011axis;":[285],"conditions":[292],"parameters":[295,315,346],"established.":[297],"Based":[298],"results,":[301],"boundedness":[302],"shown":[306],"via":[307],"contradiction.":[308],"Closedness":[309],"follows":[310],"plus":[316],"closedness":[317],"physical":[320,348,379],"space;":[322],"Heine\u2011Borel":[324],"theorem":[325,330],"yields":[326],"\\(\\Theta_{valid}\\).":[332],"Moreover,":[333],"finite":[335],"uniform":[336],"constant":[339],"product":[342],"valid":[345],"states":[349],"Explicit":[352],"criteria":[354],"discretization":[357],"derived":[359],"support":[361],"convergence":[362],"analysis":[363],"error":[365],"estimation":[366],"finite\u2011element,":[368],"IMEX":[369],"other":[371],"schemes.":[373],"work":[375],"elevates":[376],"axiomatic":[380],"intuition":[381],"rigorously":[384],"well\u2011posed":[385],"under":[388],"functional\u2011analysis,":[389],"delivering":[390],"unconditional\u2011convergence":[392],"license":[394],"chips,":[398],"brain\u2011computer\u2011interface":[399],"hardware":[400],"open":[402],"dissipative":[403],"complex\u2011system":[404],"simulations.":[405],"Appendices":[406],"cover":[407],"definition":[408],"spaces,":[411],"review":[412],"analytic":[414],"semigroups":[415],"conditions.":[419],"list":[424],"corpus":[428],"together":[429],"copyright":[431],"registration":[432],"indices":[433],"attached":[435],"at":[436],"end.":[438]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-26T00:00:00"}
