ANISOTROPIC VANISHING DIFFUSION METHOD APPLIED TO GENUINELY NONLINEAR FORWARD-BACKWARD ULTRA-PARABOLIC EQUATIONS

被引：1

作者：

Kuznetsov, Ivan V. ^{[1
,2
]}

Sazhenkov, Sergey A. ^{[1
,2
]}

机构：

[1] Novosibirsk State Univ, Pirogova St 2, Novosibirsk 630090, Russia

[2] Russian Acad Sci, Siberian Div, Lavrentyev Inst Hydrodynam, Pr Acad Lavrentyeva 15, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2018年 / 15卷

基金：

俄罗斯基础研究基金会;

关键词：

forward-backward ultra-parabolic equation; entropy solution; kinetic solution;

D O I：

10.17377/semi.2018.15.094

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The results formulated in (I.V. Kuznetsov, Sib. Elect. Math. Rep. 14 (2017), 710-731) are extended onto the multi-time case. We prove existence and uniqueness of kinetic solutions to genuinely nonlinear forward-backward ultra-parabolic equations and show that kinetic solutions do not depend on the anisotropic elliptic regularization.

引用

页码：1158 / 1173

页数：16

共 39 条

[1] Entropy solutions to a strongly degenerate anisotropic convection-diffusion equation with application to utility theory [J].

Amadori, AL ;

Natalini, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 284 (02) :511-531

[2]

Antontsev SN, 2017, SIB ELECTRON MATH RE, V14, P774, DOI 10.17377/semi.2017.14.066

[3] Singular Perturbations of Forward-Backward p-Parabolic Equations [J].

Antontsev S.N. ;

Kuznetsov I.V. .

Journal of Elliptic and Parabolic Equations, 2016, 2 (1-2) :357-370

[4]

Antontsev S. N., 1990, BOUND VALUE PROBL

[5]

Antontsev S. N., 2015, EVOLUTION PDES NONST

[6]

Bardos C., 1979, COMMUN PART DIFF EQ, V4, P1017, DOI [DOI 10.1080/03605307908820117, 10.1080/03605307908820117]

[7]

Bocharov O B, 1978, DYNAMIKA SPLOSHNOY S, V37, P27

[8]

Chipot M., 2011, J MATH SCI-U TOKYO, V176, P828

[9]

Chipot M. M., 2016, ASYMPTOTIC ISSUES SO

[10] Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation [J].

Coclite, G. M. ;

Karlsen, K. H. ;

Kwon, Y. -S. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (12) :3823-3857

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