Singular limits of the quasi-linear Kolmogorov-type equation with a source term Full article
| Journal |
Journal of Hyperbolic Differential Equations
ISSN: 0219-8916 |
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| Output data | Year: 2021, Volume: 18, Number: 04, Pages: 789-856 Pages count : 68 DOI: 10.1142/s0219891621500247 | ||||
| Tags | entropy solution; genuine nonlinearity condition; impulsive equation; kinetic formulation; Ultra-parabolic equation | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0010 |
Abstract:
Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the
Kolmogorov-type genuinely nonlinear degenerate hyperbolic-parabolic (ultra-parabolic) equation with a smooth source term is established. In addition, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is fulfilled and rigorously justified. The proofs rely on the method of kinetic equation and on the compensated compactness techniques for genuinely nonlinear equations.
Cite:
Kuznetsov I.
, Sazhenkov S.
Singular limits of the quasi-linear Kolmogorov-type equation with a source term
Journal of Hyperbolic Differential Equations. 2021. V.18. N04. P.789-856. DOI: 10.1142/s0219891621500247 WOS Scopus РИНЦ OpenAlex
Singular limits of the quasi-linear Kolmogorov-type equation with a source term
Journal of Hyperbolic Differential Equations. 2021. V.18. N04. P.789-856. DOI: 10.1142/s0219891621500247 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 25, 2020 |
| Accepted: | Dec 6, 2021 |
| Published print: | Feb 9, 2022 |
Identifiers:
| Web of science: | WOS:000753449300001 |
| Scopus: | 2-s2.0-85124529918 |
| Elibrary: | 48133089 |
| OpenAlex: | W2958652826 |