О единственности решения задачи Коши для квазилинейного уравнения первого порядка с одной допустимой строго выпуклой энтропией
Е. Ю. Панов

Эта публикация цитируется в следующих статьяx:

1. Jan Giesselmann, Sam Krupa, “Theory of shifts, shocks, and the intimate connections to 𝐿²-type A posteriori error analysis of numerical schemes for hyperbolic problems”, Math. Comp., 2025  
2. Jeffrey Cheng, “𝐿²-stability and minimal entropy conditions for scalar conservation laws with concave-convex fluxes”, Quart. Appl. Math., 2025  
3. Florent Renac, “Maximum principle preserving and entropy stable time implicit DGSEM for nonlinear scalar conservation laws”, ESAIM: M2AN, 59:5 (2025), 2583  
4. Flavia Smarrazzo, “On a Nonlinear Hyperbolic–Elliptic System Modeling Chemotaxis”, Mathematics, 13:21 (2025), 3523  
5. Jan Friedrich, Simone Göttlich, Alexander Keimer, Lukas Pflug, “Conservation Laws with Nonlocal Velocity: The Singular Limit Problem”, SIAM J. Appl. Math., 84:2 (2024), 497  
6. Aidan Chaumet, Jan Giesselmann, “Improving Weak PINNs for Hyperbolic Conservation Laws: Dual Norm Computation, Boundary Conditions and Systems”, The SMAI Journal of computational mathematics, 10 (2024), 373  
7. Gaowei Cao, Gui-Qiang Chen, “Minimal entropy conditions for scalar conservation laws with general convex fluxes”, Quart. Appl. Math., 81:3 (2023), 567  
8. Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla, “Conservation laws and Hamilton–Jacobi equations with space inhomogeneity”, J. Evol. Equ., 23:3 (2023)  
9. Alexander Keimer, Lukas Pflug, “On the singular limit problem for a discontinuous nonlocal conservation law”, Nonlinear Analysis, 237 (2023), 113381  
10. Geng Chen, Sam G. Krupa, Alexis F. Vasseur, “Uniqueness and Weak-BV Stability for $2\times 2$ Conservation Laws”, Arch Rational Mech Anal, 246:1 (2022), 299  
11. Philip Isett, “Nonuniqueness and Existence of Continuous, Globally Dissipative Euler Flows”, Arch Rational Mech Anal, 244:3 (2022), 1223  
12. E. Abreu, R. De la cruz, J. C. Juajibioy, W. Lambert, “Lagrangian-Eulerian Approach for Nonlocal Conservation Laws”, J Dyn Diff Equat, 2022  
13. Philippe G. LeFloch, Hendrik Ranocha, “Kinetic Functions for Nonclassical Shocks, Entropy Stability, and Discrete Summation by Parts”, J Sci Comput, 87:2 (2021)  
14. Edwige Godlewski, Pierre-Arnaud Raviart, Applied Mathematical Sciences, 118, Numerical Approximation of Hyperbolic Systems of Conservation Laws, 2021, 1  
15. Hendrik Ranocha, “Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives”, Bit Numer Math, 59:2 (2019), 547  
16. Sanghyun Lee, Mary F. Wheeler, “Enriched Galerkin methods for two-phase flow in porous media with capillary pressure”, Journal of Computational Physics, 367 (2018), 65  
17. Tianheng Chen, Chi-Wang Shu, “Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws”, Journal of Computational Physics, 345 (2017), 427  
18. Sanghyun Lee, Mary F. Wheeler, “Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization”, Journal of Computational Physics, 331 (2017), 19  
19. Е. Ю. Панов, “Об асимптотике при больших временах периодических обобщенных энтропийных решений скалярных законов сохранения”, Матем. заметки, 100:1 (2016), 133–143        ; E. Yu. Panov, “Long Time Asymptotics of Periodic Generalized Entropy Solutions of Scalar Conservation Laws”, Math. Notes, 100:1 (2016), 113–122    
20. Claude Bardos, Eitan Tadmor, “Stability and spectral convergence of Fourier method for nonlinear problems: on the shortcomings of the $2/3$ 2 / 3 de-aliasing method”, Numer. Math., 129:4 (2015), 749  
21. Е. А. Колпакова, “Обобщенный метод характеристик в теории уравнений Гамильтона–Якоби и законов сохранения”, Тр. ИММ УрО РАН, 16, № 5, 2010, 95–102    
22. LAURA CARAVENNA, “AN ENTROPY BASED GLIMM-TYPE FUNCTIONAL”, J. Hyper. Differential Equations, 05:03 (2008), 643  
23. Camillo De Lellis, Felix Otto, Michael Westdickenberg, “Minimal entropy conditions for Burgers equation”, Quart. Appl. Math., 62:4 (2004), 687