EXISTENCE OF ENTROPY MEASURE-VALUED SOLUTIONS FOR FORWARD-BACKWARD P-PARABOLIC EQUATIONS Full article
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Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304 |
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| Output data | Year: 2017, Volume: 14, Pages: 774-793 Pages count : 20 DOI: 10.17377/semi.2017.14.066 | ||
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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.
Cite:
Antontsev S.N.
, Kuznetsov I.V.
EXISTENCE OF ENTROPY MEASURE-VALUED SOLUTIONS FOR FORWARD-BACKWARD P-PARABOLIC EQUATIONS
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2017. V.14. P.774-793. DOI: 10.17377/semi.2017.14.066 WOS Scopus РИНЦ
EXISTENCE OF ENTROPY MEASURE-VALUED SOLUTIONS FOR FORWARD-BACKWARD P-PARABOLIC EQUATIONS
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2017. V.14. P.774-793. DOI: 10.17377/semi.2017.14.066 WOS Scopus РИНЦ
Dates:
| Submitted: | May 28, 2017 |
| Accepted: | Aug 16, 2017 |
Identifiers:
| Web of science: | WOS:000407792200066 |
| Scopus: | 2-s2.0-85074578845 |
| Elibrary: | 54806782 |