The one-dimensional impulsive Barenblatt--Zheltov--Kochina equation with a transition layer Full article
| Journal |
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304 |
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| Output data | Year: 2022, Volume: 19, Number: 2, Pages: 724-740 Pages count : 17 DOI: 10.33048/semi.2022.19.060 | ||||
| Tags | PSEUDOPARABOLIC EQUATION, IMPULSIVE EQUATION, STRONG SOLUTION, FOURIER SERIES, TRANSITION LAYER | ||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0010 |
| 2 | Министерство науки и высшего образования Российской Федерации | FZMW-2020-0008 |
Abstract:
The initial-boundary value problem for the one-dimensional impulsive pseudoparabolic equation is studied. As a coefficient in the second-order diffusion term, this equation contains the smoothed Dirac delta-function concentrated at some time moment. From a physical viewpoint, such term allows to describe impulsive pressure drop phenomena in filtration problems. Existence and uniqueness of solutions for fixed values of the small parameter of smoothing is proved. After this, the limiting passage as the small parameter tends to zero is fulfilled and rigorously justified. As the result, the limit instantaneous impulsive microscopic-macroscopic model is established. This model is well-posed and involves the additional equation on a transition layer posed on a `very fast' timescale.
Cite:
Kuznetsov I.V.
, Sazhenkov S.A.
The one-dimensional impulsive Barenblatt--Zheltov--Kochina equation with a transition layer
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2022. V.19. N2. P.724-740. DOI: 10.33048/semi.2022.19.060 WOS Scopus РИНЦ
The one-dimensional impulsive Barenblatt--Zheltov--Kochina equation with a transition layer
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2022. V.19. N2. P.724-740. DOI: 10.33048/semi.2022.19.060 WOS Scopus РИНЦ
Dates:
| Submitted: | Apr 26, 2022 |
| Accepted: | Nov 11, 2022 |
Identifiers:
| Web of science: | WOS:000886649600026 |
| Scopus: | 2-s2.0-85145864771 |
| Elibrary: | 50336846 |