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 Mat. Sb., 1999, Volume 190, Number 3, Pages 109–128 (Mi msb395)

Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation

E. Yu. Panov

Novgorod State University after Yaroslav the Wise

Abstract: Sequences of measure-valued solutions of a non-degenerate quasilinear equation of the first order are shown to be strongly precompact in the general case, when the flow functions contain independent variables and are merely continuous.

DOI: https://doi.org/10.4213/sm395

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English version:
Sbornik: Mathematics, 1999, 190:3, 427–446

Bibliographic databases:

UDC: 517.95
MSC: Primary 35F20, 35B30; Secondary 35D99

Citation: E. Yu. Panov, “Property of strong precompactness for bounded sets of measure-valued solutions of a first-order quasilinear equation”, Mat. Sb., 190:3 (1999), 109–128; Sb. Math., 190:3 (1999), 427–446

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb395
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sazhenkov, S, “A Cauchy problem for the Tartar equation”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 132 (2002), 395
2. Panov, EY, “Existence of strong traces for generalized solutions of multidimensional scalar conservation laws”, Journal of Hyperbolic Differential Equations, 2:4 (2005), 885
3. S. A. Sazhenkov, “The genuinely nonlinear Graetz–Nusselt ultraparabolic equation”, Siberian Math. J., 47:2 (2006), 355–375
4. Panov, EY, “Existence of strong traces for quasi-solutions of multidimensional conservation laws”, Journal of Hyperbolic Differential Equations, 4:4 (2007), 729
5. Karlsen, KH, “On the existence and compactness of a two-dimensional resonant system of conservation laws”, Communications in Mathematical Sciences, 5:2 (2007), 253
6. S. A. Sazhenkov, “Entropy solutions to the Verigin ultraparabolic problem”, Siberian Math. J., 49:2 (2008), 362–374
7. Panov E.Y., “Existence of strong traces for quasisolutions of scalar conservation laws”, Hyperbolic Problems: Theory, Numerics, Applications - Proceedings of the 11Th International Conference on Hyperbolic Problems, 2008, 807–815
8. Holden, H, “STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION”, Acta Mathematica Scientia, 29:6 (2009), 1573
9. Aleksic, J, “Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media”, Journal of Evolution Equations, 9:4 (2009), 809
10. Panov, EY, “On the strong pre-compactness property for entropy solutions of a degenerate elliptic equation with discontinuous flux”, Journal of Differential Equations, 247:10 (2009), 2821
11. H. Holden, K. H. Karlsen, D. Mitrovic, “Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function”, International Journal of Differential Equations, 2009 (2009), 1
12. Panov, EY, “Existence and Strong Pre-compactness Properties for Entropy Solutions of a First-Order Quasilinear Equation with Discontinuous Flux”, Archive For Rational Mechanics and Analysis, 195:2 (2010), 643
13. Julien Jimenez, “Mathematical analysis of a scalar multidimensional conservation law with discontinuous flux”, J. Evol. Equ, 2011
14. Panov E.Yu., “On Decay of Periodic Entropy Solutions to a Scalar Conservation Law”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 30:6 (2013), 997–1007
15. E. Yu. Panov, “Stabilization Property of Periodic Generalized Entropy Solutions to Quasilinear First Order Equations”, J Math Sci, 2015
16. Panov E.Yu., “On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws”, Netw. Heterog. Media, 11:2, SI (2016), 349–367
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