Singular limits of the quasi-linear Kolmogorov-type equation with a source term
Analysis of PDEs
2019-07-10 v1
Abstract
Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, 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.
Keywords
Cite
@article{arxiv.1907.04250,
title = {Singular limits of the quasi-linear Kolmogorov-type equation with a source term},
author = {Ivan Kuznetsov and Sergey Sazhenkov},
journal= {arXiv preprint arXiv:1907.04250},
year = {2019}
}