Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term

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Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term. / Kuznetsov, I. V.; Sazhenkov, S. A.

In: Journal of Physics: Conference Series, Vol. 1666, No. 1, 012025, 20.11.2020.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{b60bdcd9b2b64ee1ae404e1ba08a7489,

title = "Entropy solutions of an ultra-parabolic equation with the one-sided Dirac delta function as the minor term",

abstract = "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.",

author = "Kuznetsov, {I. V.} and Sazhenkov, {S. A.}",

note = "Publisher Copyright: {\textcopyright} Published under licence by IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics ; Conference date: 07-09-2020 Through 11-09-2020",

year = "2020",

month = nov,

day = "20",

doi = "10.1088/1742-6596/1666/1/012025",

language = "English",

volume = "1666",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

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.

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