Результаты исследований: Научные публикации в периодических изданиях › статья по материалам конференции › Рецензирование
Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term. / Kuznetsov, I. V.; Sazhenkov, S. A.
в: Journal of Physics: Conference Series, Том 1666, № 1, 012025, 20.11.2020.Результаты исследований: Научные публикации в периодических изданиях › статья по материалам конференции › Рецензирование
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TY - JOUR
T1 - Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term
AU - Kuznetsov, I. V.
AU - Sazhenkov, S. A.
N1 - Publisher Copyright: © Published under licence by IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/20
Y1 - 2020/11/20
N2 - The Cauchy-Dirichlet problem for the genuinely nonlinear ultra-parabolic equation with the piece-wise smooth minor term is considered. The minor term depends on a small positive parameter and collapses to the one-sided Dirac delta function as this parameter tends to zero. As the result, we arrive at the limiting initial-boundary value problem for the impulsive ultra-parabolic equation. The peculiarity is that the standard entropy solution of the problem for the impulsive equation generally is not unique. In this report, we propose a rule for selecting the 'proper' entropy solution, relying on the limiting procedure in the original problem incorporating the smooth minor term.
AB - The Cauchy-Dirichlet problem for the genuinely nonlinear ultra-parabolic equation with the piece-wise smooth minor term is considered. The minor term depends on a small positive parameter and collapses to the one-sided Dirac delta function as this parameter tends to zero. As the result, we arrive at the limiting initial-boundary value problem for the impulsive ultra-parabolic equation. The peculiarity is that the standard entropy solution of the problem for the impulsive equation generally is not unique. In this report, we propose a rule for selecting the 'proper' entropy solution, relying on the limiting procedure in the original problem incorporating the smooth minor term.
UR - http://www.scopus.com/inward/record.url?scp=85097094374&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1666/1/012025
DO - 10.1088/1742-6596/1666/1/012025
M3 - Conference article
AN - SCOPUS:85097094374
VL - 1666
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012025
T2 - 9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics
Y2 - 7 September 2020 through 11 September 2020
ER -
ID: 26205697