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Singular limits of the quasi-linear Kolmogorov-type equation with a source term. / Kuznetsov, Ivan; Sazhenkov, Sergey.

In: Journal of Hyperbolic Differential Equations, Vol. 18, No. 4, 01.12.2021, p. 789-856.

Research output: Contribution to journal › Article › peer-review

Harvard

Kuznetsov, I & Sazhenkov, S 2021, 'Singular limits of the quasi-linear Kolmogorov-type equation with a source term', Journal of Hyperbolic Differential Equations, vol. 18, no. 4, pp. 789-856. https://doi.org/10.1142/S0219891621500247

APA

Kuznetsov, I., & Sazhenkov, S. (2021). Singular limits of the quasi-linear Kolmogorov-type equation with a source term. Journal of Hyperbolic Differential Equations, 18(4), 789-856. https://doi.org/10.1142/S0219891621500247

Vancouver

Kuznetsov I, Sazhenkov S. Singular limits of the quasi-linear Kolmogorov-type equation with a source term. Journal of Hyperbolic Differential Equations. 2021 Dec 1;18(4):789-856. doi: 10.1142/S0219891621500247

Author

Kuznetsov, Ivan ; Sazhenkov, Sergey. / Singular limits of the quasi-linear Kolmogorov-type equation with a source term. In: Journal of Hyperbolic Differential Equations. 2021 ; Vol. 18, No. 4. pp. 789-856.

BibTeX

@article{77b26d948ffb4078827fa6468e502a6e,
title = "Singular limits of the quasi-linear Kolmogorov-type equation with a source term",
abstract = "Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with 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 investigated and the formal limit is rigorously justified. Our proofs rely on the use of kinetic equations and the compensated compactness method for genuinely nonlinear balance laws.",
keywords = "entropy solution, genuine nonlinearity condition, impulsive equation, kinetic formulation, Ultra-parabolic equation",
author = "Ivan Kuznetsov and Sergey Sazhenkov",
note = "Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company",
year = "2021",
month = dec,
day = "1",
doi = "10.1142/S0219891621500247",
language = "English",
volume = "18",
pages = "789--856",
journal = "Journal of Hyperbolic Differential Equations",
issn = "0219-8916",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "4",

}

RIS

TY - JOUR

T1 - Singular limits of the quasi-linear Kolmogorov-type equation with a source term

AU - Kuznetsov, Ivan

AU - Sazhenkov, Sergey

N1 - Publisher Copyright: © 2021 World Scientific Publishing Company

PY - 2021/12/1

Y1 - 2021/12/1

N2 - Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with 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 investigated and the formal limit is rigorously justified. Our proofs rely on the use of kinetic equations and the compensated compactness method for genuinely nonlinear balance laws.

AB - Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with 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 investigated and the formal limit is rigorously justified. Our proofs rely on the use of kinetic equations and the compensated compactness method for genuinely nonlinear balance laws.

KW - entropy solution

KW - genuine nonlinearity condition

KW - impulsive equation

KW - kinetic formulation

KW - Ultra-parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=85124529918&partnerID=8YFLogxK

U2 - 10.1142/S0219891621500247

DO - 10.1142/S0219891621500247

M3 - Article

AN - SCOPUS:85124529918

VL - 18

SP - 789

EP - 856

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

SN - 0219-8916

IS - 4

ER -

ID: 35541523