Mathematical effects of linear visco-elasticity in quasi-static Biot models

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dc.contributor.authorBociu, Lorena
dc.contributor.authorMuha,  Boris
dc.contributor.authorWebster,  Justin T.
dc.date.accessioned2022-10-07T15:29:46Z
dc.date.available2022-10-07T15:29:46Z
dc.date.issued2023-06-20
dc.description.abstractWe investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of visco-elasticity in the context of the quasi-static Biot equations. The full, coupled pressure-displacement presentation of the system is utilized, as well as the framework of implicit, degenerate evolution equations, to demonstrate such effects and characterize linear poro-visco-elastic systems. We consider a simple presentation of the dynamics (with convenient boundary conditions, etc.) for clarity in exposition across several relevant parameter ranges. Clear well-posedness results are provided, with associated a priori estimates on the solutions. In addition, precise statements of admissible initial conditions in each scenario are given.
dc.description.sponsorshipAuthor 1 was supported by NSF-DMS 1555062 (CAREER). Author 2 was supported by the Croatian Science Foundation project IP-2019-04-1140. Author 3 was partially supported by NSF-DMS 1907620.en_US
dc.description.urihttps://www.sciencedirect.com/science/article/pii/S0022247X23004651en_US
dc.format.extent20 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprintsen_US
dc.identifierdoi:10.13016/m28gtj-ejuw
dc.identifier.citationBociu, Lorena, Boris Muha, and Justin T. Webster. “Mathematical Effects of Linear Visco-Elasticity in Quasi-Static Biot Models.” Journal of Mathematical Analysis and Applications 527, no. 2 (November 15, 2023): 127462. https://doi.org/10.1016/j.jmaa.2023.127462.
dc.identifier.urihttps://doi.org/10.1016/j.jmaa.2023.127462
dc.identifier.urihttp://hdl.handle.net/11603/26117
dc.language.isoen_USen_US
dc.publisherElsevier
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.en_US
dc.titleMathematical effects of linear visco-elasticity in quasi-static Biot modelsen_US
dc.title.alternativeThe Mathematical Effects of Visco-elasticity in Quasi-static Biot Models
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-2443-3789en_US

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