Mathematical effects of linear visco-elasticity in quasi-static Biot models
| dc.contributor.author | Bociu, Lorena | |
| dc.contributor.author | Muha, Boris | |
| dc.contributor.author | Webster, Justin T. | |
| dc.date.accessioned | 2022-10-07T15:29:46Z | |
| dc.date.available | 2022-10-07T15:29:46Z | |
| dc.date.issued | 2023-06-20 | |
| dc.description.abstract | We 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.sponsorship | Author 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.uri | https://www.sciencedirect.com/science/article/pii/S0022247X23004651 | en_US |
| dc.format.extent | 20 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m28gtj-ejuw | |
| dc.identifier.citation | Bociu, 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.uri | https://doi.org/10.1016/j.jmaa.2023.127462 | |
| dc.identifier.uri | http://hdl.handle.net/11603/26117 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Elsevier | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This 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.title | Mathematical effects of linear visco-elasticity in quasi-static Biot models | en_US |
| dc.title.alternative | The Mathematical Effects of Visco-elasticity in Quasi-static Biot Models | |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-2443-3789 | en_US |