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

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https://www.sciencedirect.com/science/article/pii/S0022247X23004651

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https://doi.org/10.1016/j.jmaa.2023.127462
 http://hdl.handle.net/11603/26117

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0002-2443-3789

Date

2023-06-20

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journal articles
preprints
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Citation of Original Publication

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.

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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.