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Existence of entropy measure-valued solutions for forward-backward p-parabolic equations. / Antontsev, Stanislav N.; Kuznetsov, Ivan V.

In: Сибирские электронные математические известия, Vol. 14, 01.01.2017, p. 774-793.

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

Harvard

Antontsev, SN & Kuznetsov, IV 2017, 'Existence of entropy measure-valued solutions for forward-backward p-parabolic equations', Сибирские электронные математические известия, vol. 14, pp. 774-793. https://doi.org/10.17377/semi.2017.14.066

APA

Antontsev, S. N., & Kuznetsov, I. V. (2017). Existence of entropy measure-valued solutions for forward-backward p-parabolic equations. Сибирские электронные математические известия, 14, 774-793. https://doi.org/10.17377/semi.2017.14.066

Vancouver

Antontsev SN, Kuznetsov IV. Existence of entropy measure-valued solutions for forward-backward p-parabolic equations. Сибирские электронные математические известия. 2017 Jan 1;14:774-793. doi: 10.17377/semi.2017.14.066

Author

Antontsev, Stanislav N. ; Kuznetsov, Ivan V. / Existence of entropy measure-valued solutions for forward-backward p-parabolic equations. In: Сибирские электронные математические известия. 2017 ; Vol. 14. pp. 774-793.

BibTeX

@article{d94c2fac9c6c41e9839889b4908b6a90,
title = "Existence of entropy measure-valued solutions for forward-backward p-parabolic equations",
abstract = "In this paper we have proved that the Dirichlet problem for the forward-backward p-parabolic equation has an entropy measurevalued solution which has been obtained as a singular limit of weak solutions and their gradients to the Dirichlet problem for the elliptic equation containing the anisotropic (p, 2)-Laplace operator. In order to guarantee the existence of entropy measure-valued solutions, the initial and final conditions should be formulated in the form of integral inequalities. This means that an entropy measure-valued solution can deviate from both initial and final data on the boundary. Moreover, a gradient Young measure appears in the representation of an entropy measurevalued solution. The uniqueness of entropy measure-valued solutions is still an open question.",
keywords = "Anisotropic Laplace operator, Entropy measure-valued solution, Forward-backward parabolic equation, Gradient Young measure",
author = "Antontsev, {Stanislav N.} and Kuznetsov, {Ivan V.}",
year = "2017",
month = jan,
day = "1",
doi = "10.17377/semi.2017.14.066",
language = "English",
volume = "14",
pages = "774--793",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Existence of entropy measure-valued solutions for forward-backward p-parabolic equations

AU - Antontsev, Stanislav N.

AU - Kuznetsov, Ivan V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper we have proved that the Dirichlet problem for the forward-backward p-parabolic equation has an entropy measurevalued solution which has been obtained as a singular limit of weak solutions and their gradients to the Dirichlet problem for the elliptic equation containing the anisotropic (p, 2)-Laplace operator. In order to guarantee the existence of entropy measure-valued solutions, the initial and final conditions should be formulated in the form of integral inequalities. This means that an entropy measure-valued solution can deviate from both initial and final data on the boundary. Moreover, a gradient Young measure appears in the representation of an entropy measurevalued solution. The uniqueness of entropy measure-valued solutions is still an open question.

AB - In this paper we have proved that the Dirichlet problem for the forward-backward p-parabolic equation has an entropy measurevalued solution which has been obtained as a singular limit of weak solutions and their gradients to the Dirichlet problem for the elliptic equation containing the anisotropic (p, 2)-Laplace operator. In order to guarantee the existence of entropy measure-valued solutions, the initial and final conditions should be formulated in the form of integral inequalities. This means that an entropy measure-valued solution can deviate from both initial and final data on the boundary. Moreover, a gradient Young measure appears in the representation of an entropy measurevalued solution. The uniqueness of entropy measure-valued solutions is still an open question.

KW - Anisotropic Laplace operator

KW - Entropy measure-valued solution

KW - Forward-backward parabolic equation

KW - Gradient Young measure

UR - http://www.scopus.com/inward/record.url?scp=85074578845&partnerID=8YFLogxK

U2 - 10.17377/semi.2017.14.066

DO - 10.17377/semi.2017.14.066

M3 - Article

AN - SCOPUS:85074578845

VL - 14

SP - 774

EP - 793

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 22318408