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Stochastically forced cardiac bidomain model

hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierCenter of Mathematics for Applications [Oslo] [CMA]
dc.contributor.authorKARLSEN, Kenneth Hvistendahl
dc.date2019
dc.date.accessioned2024-04-04T03:00:56Z
dc.date.available2024-04-04T03:00:56Z
dc.date.issued2019
dc.identifier.issn0304-4149
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192857
dc.description.abstractEnThe bidomain system of degenerate reaction–diffusion equations is a well-established spatial model of electrical activity in cardiac tissue, with “reaction” linked to the cellular action potential and “diffusion” representing current flow between cells. The purpose of this paper is to introduce a “stochastically forced” version of the bidomain model that accounts for various random effects. We establish the existence of martingale (probabilistic weak) solutions to the stochastic bidomain model. The result is proved by means of an auxiliary nondegenerate system and the Faedo–Galerkin method. To prove convergence of the approximate solutions, we use the stochastic compactness method and Skorokhod–Jakubowski a.s. representations. Finally, via a pathwise uniqueness result, we conclude that the martingale solutions are pathwise (i.e., probabilistic strong) solutions.
dc.language.isoen
dc.publisherElsevier
dc.title.enStochastically forced cardiac bidomain model
dc.typeArticle de revue
dc.identifier.doi10.1016/j.spa.2019.03.001
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halSciences du Vivant [q-bio]
dc.subject.halSciences du Vivant [q-bio]/Biologie cellulaire
dc.subject.halMathématiques [math]/Mathématiques générales [math.GM]
dc.identifier.arxiv1803.08537
bordeaux.journalStochastic Processes and their Applications
bordeaux.page5312-5363
bordeaux.volume129
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue12
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02142024
hal.version1
hal.popularoui
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02142024v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Stochastic%20Processes%20and%20their%20Applications&rft.date=2019&rft.volume=129&rft.issue=12&rft.spage=5312-5363&rft.epage=5312-5363&rft.eissn=0304-4149&rft.issn=0304-4149&rft.au=BENDAHMANE,%20Mostafa&KARLSEN,%20Kenneth%20Hvistendahl&rft.genre=article


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