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

Autor:	Ivan Kuznetsov, Sergey Sazhenkov
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs General Mathematics FOS: Mathematics 35D30 35K70 35R12 Analysis Analysis of PDEs (math.AP)
Zdroj:	Journal of Hyperbolic Differential Equations. 18:789-856
ISSN:	1793-6993 0219-8916
DOI:	10.1142/s0219891621500247
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6b83503fc0d7b1fe4d0b2f4a666aa86 https://doi.org/10.1142/s0219891621500247 Zobrazit plný text záznamu