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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2013, Volume 54, Issue 2, Pages 97–105
(Mi pmtf1202)
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This article is cited in 22 scientific papers (total in 22 papers)
Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration
A. L. Kazakov, A. A. Lempert Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Science, Irkutsk, 664033, Russia
Abstract:
The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.
Keywords:
nonlinear filtration, partial differential equations, boundary-value problem, existence and uniqueness theorem, series, convergence.
Received: 08.08.2012
Citation:
A. L. Kazakov, A. A. Lempert, “Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration”, Prikl. Mekh. Tekh. Fiz., 54:2 (2013), 97–105; J. Appl. Mech. Tech. Phys., 54:2 (2013), 251–258
Linking options:
https://www.mathnet.ru/eng/pmtf1202 https://www.mathnet.ru/eng/pmtf/v54/i2/p97
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Abstract page: | 57 | Full-text PDF : | 17 |
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