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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 3, Pages 556–577
DOI: https://doi.org/10.33048/smzh.2019.60.307 (Mi smj3095) 		 
On the solvability of some dynamic poroelastic problems

M. P. Vishnevskiiab, V. I. Priimenkob

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b State University of Norte Fluminense, Brazil
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DOI: https://doi.org/10.33048/smzh.2019.60.307
Abstract: We consider the direct problems for poroelasticity equations. In the low-frequency approximation we prove existence and uniqueness theorems for the solution to a certain mixed problem. In the high-frequency approximation we establish the uniqueness of a weak solution to the mixed problem and its continuous dependence on the data in the cases of bounded and unbounded temporal intervals and for however many spatial variables.
Keywords: poroelasticity equations, dynamic permeability, mixed problem, existence, uniqueness, stability.
Received: 10.10.2017
Revised: 10.10.2017
Accepted: 17.10.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 3, Pages 429–449
DOI: https://doi.org/10.1134/S0037446619030078
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35R30
Language: Russian
Citation: M. P. Vishnevskii, V. I. Priimenko, “On the solvability of some dynamic poroelastic problems”, Sibirsk. Mat. Zh., 60:3 (2019), 556–577; Siberian Math. J., 60:3 (2019), 429–449
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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