The solution of an initial-boundary value problem of the filtration theory with nonlocal boundary condition
Articles
Ludmila Serbina
Institute of Applied Mathematics and Automation, RAS, Russia
Published 2014-10-30
https://doi.org/10.15388/NA.2014.3.12
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Keywords

motion of groundwater
Boussinesq's equation
equations of mixed type
Lavrentiev– Bitsadze equation
nonlocal problems
Samarskii condition
initial and boundary value problems

How to Cite

Serbina, L. (2014) “The solution of an initial-boundary value problem of the filtration theory with nonlocal boundary condition”, Nonlinear Analysis: Modelling and Control, 19(3), pp. 488–502. doi:10.15388/NA.2014.3.12.

Abstract

The nonlocal initial and boundary value problem for Lavrentiev–Bitsadze equation is considered. By this problem the nonstacionary one-dimentional motion of a groundwater with horizontal stopping is modeling. The existence and the uniqueness of the classical (in the elliptic part of the domain) and generalized (in the hyperbolic part of the domain) solution of the considered problem is proved.

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