Nonlinear Quasi-static Poroelasticity
| dc.contributor.author | Bociu, Lorena | |
| dc.contributor.author | Webster, Justin | |
| dc.date.accessioned | 2020-12-14T16:30:36Z | |
| dc.date.available | 2020-12-14T16:30:36Z | |
| dc.date.issued | 2021-06-10 | |
| dc.description.abstract | We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a model has been analyzed previously from the point of view of constructing weak solutions through a fully discretized approach. In this treatment, we consider simplified Dirichlet type boundary conditions in the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is natural and based on a priori estimates, a requisite feature in addressing the nonlinearity. This is in contrast to previous work which exploits linearity or monotonicity in the permeability, both of which are not available here. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument in for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions. | en_US |
| dc.description.uri | https://www.sciencedirect.com/science/article/pii/S0022039621003703 | en_US |
| dc.format.extent | 31 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | |
| dc.identifier | doi:10.13016/m2lixb-vhk1 | |
| dc.identifier.citation | Bociu, Lorena, & Justin T.Webster. "Nonlinear quasi-static poroelasticity." Journal of Differential Equations 296 (25 September 2021): 242-278. https://doi.org/10.1016/j.jde.2021.05.060 | en_US |
| dc.identifier.uri | http://hdl.handle.net/11603/20253 | |
| dc.identifier.uri | https://doi.org/10.1016/j.jde.2021.05.060 | |
| 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. | |
| dc.title | Nonlinear Quasi-static Poroelasticity | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-2443-3789 |