Geodesic
A model of liquid level measurements
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2115-2124

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A model of measuring the level of a viscous incompressible liquid in a tank as based on the liquid level in a measuring tube is investigated. The tank is in the field of gravity, and the tank liquid level varies according to some law. As a result, a Dirichlet boundary value problem for a nonlinear integrodifferential equation of parabolic type is obtained. A global existence and uniqueness theorem is proved for a weak solution of the problem. In the case of a tank level decreasing linearly with time, it is shown numerically that the liquid level in the measuring tube oscillates with a decaying amplitude with respect to the tank level. 
@article{ZVMMF_2016_56_12_a12,
     author = {O. P. Filatov},
     title = {A model of liquid level measurements},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2115--2124},
     publisher = {mathdoc},
     volume = {56},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a12/}
}
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O. P. Filatov. A model of liquid level measurements. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2115-2124. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a12/