Bressan, Alberto; Guerra, Graziano Unique solutions to hyperbolic conservation laws with a strictly convex entropy. (English) Zbl 07806933 J. Differ. Equations 387, 432-447 (2024). MSC: 35L65 35A02 35L45 PDFBibTeX XMLCite \textit{A. Bressan} and \textit{G. Guerra}, J. Differ. Equations 387, 432--447 (2024; Zbl 07806933) Full Text: DOI arXiv
Golding, William M.; Krupa, Sam G.; Vasseur, Alexis F. Sharp \(a\)-contraction estimates for small extremal shocks. (English) Zbl 07800859 J. Hyperbolic Differ. Equ. 20, No. 3, 541-602 (2023). MSC: 35L67 35L45 35L60 35Q31 PDFBibTeX XMLCite \textit{W. M. Golding} et al., J. Hyperbolic Differ. Equ. 20, No. 3, 541--602 (2023; Zbl 07800859) Full Text: DOI arXiv
Bressan, Alberto; De Lellis, Camillo A remark on the uniqueness of solutions to hyperbolic conservation laws. (English) Zbl 07771234 Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 106, 12 p. (2023). MSC: 35A02 35L45 35L65 47D06 PDFBibTeX XMLCite \textit{A. Bressan} and \textit{C. De Lellis}, Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 106, 12 p. (2023; Zbl 07771234) Full Text: DOI arXiv
Golding, William Unconditional regularity and trace results for the isentropic Euler equations with \(\gamma = 3\). (English) Zbl 1526.35098 SIAM J. Math. Anal. 55, No. 5, 5751-5781 (2023). MSC: 35B65 35L40 35L65 35Q31 PDFBibTeX XMLCite \textit{W. Golding}, SIAM J. Math. Anal. 55, No. 5, 5751--5781 (2023; Zbl 1526.35098) Full Text: DOI arXiv
Vasseur, Alexis F. A review of recent applications of the relative entropy method to discontinuous solutions of conservation laws. (English) Zbl 1516.35266 Q. Appl. Math. 81, No. 3, 553-565 (2023). MSC: 35L65 35B35 35L45 35Q31 76N15 PDFBibTeX XMLCite \textit{A. F. Vasseur}, Q. Appl. Math. 81, No. 3, 553--565 (2023; Zbl 1516.35266) Full Text: DOI
Chen, Geng; Krupa, Sam G.; Vasseur, Alexis F. Uniqueness and weak-BV stability for \(2\times 2\) conservation laws. (English) Zbl 1505.35265 Arch. Ration. Mech. Anal. 246, No. 1, 299-332 (2022). Reviewer: Evgeniy Panov (Veliky Novgorod) MSC: 35L65 35A02 35B35 PDFBibTeX XMLCite \textit{G. Chen} et al., Arch. Ration. Mech. Anal. 246, No. 1, 299--332 (2022; Zbl 1505.35265) Full Text: DOI arXiv
Abgrall, Rémi (ed.); Garavello, Mauro (ed.); Lukáčová-Medvid’ová, Mária (ed.); Trivisa, Konstantina (ed.) Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 – March 6, 2021 (hybrid meeting). (English) Zbl 1487.00026 Oberwolfach Rep. 18, No. 1, 589-661 (2021). MSC: 00B05 00B25 35-06 60-06 35L65 35L40 35L60 35R60 65M08 60H15 PDFBibTeX XMLCite \textit{R. Abgrall} (ed.) et al., Oberwolfach Rep. 18, No. 1, 589--661 (2021; Zbl 1487.00026) Full Text: DOI
Bressan, Alberto; Chiri, Maria Teresa; Shen, Wen A posteriori error estimates for numerical solutions to hyperbolic conservation laws. (English) Zbl 1472.35018 Arch. Ration. Mech. Anal. 241, No. 1, 357-402 (2021). Reviewer: Jan Giesselmann (Darmstadt) MSC: 35A35 35L02 65M08 65M15 35L65 PDFBibTeX XMLCite \textit{A. Bressan} et al., Arch. Ration. Mech. Anal. 241, No. 1, 357--402 (2021; Zbl 1472.35018) Full Text: DOI arXiv
Ghoshal, Shyam Sundar; Jana, Animesh Optimal jump set in hyperbolic conservation laws. (English) Zbl 1471.35198 J. Hyperbolic Differ. Equ. 17, No. 4, 765-784 (2020). MSC: 35L65 35B65 35L67 93B05 PDFBibTeX XMLCite \textit{S. S. Ghoshal} and \textit{A. Jana}, J. Hyperbolic Differ. Equ. 17, No. 4, 765--784 (2020; Zbl 1471.35198) Full Text: DOI arXiv
Giesselmann, Jan; Meyer, Fabian; Rohde, Christian A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. (English) Zbl 1446.65111 BIT 60, No. 3, 619-649 (2020). MSC: 65M60 65L06 65N30 65M70 65M50 65M15 35L65 35R60 62F15 PDFBibTeX XMLCite \textit{J. Giesselmann} et al., BIT 60, No. 3, 619--649 (2020; Zbl 1446.65111) Full Text: DOI arXiv
Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska Multilevel Monte Carlo front-tracking for random scalar conservation laws. (English) Zbl 1350.65008 BIT 56, No. 1, 263-292 (2016); correction ibid. 58, No. 1, 247-255 (2018). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C30 35L65 65C05 65M06 65M12 60H15 60H35 35R60 65Y20 65M75 PDFBibTeX XMLCite \textit{N. H. Risebro} et al., BIT 56, No. 1, 263--292 (2016; Zbl 1350.65008) Full Text: DOI Link
Qu, Peng; Xin, Zhouping Long time existence of entropy solutions to the one-dimensional non-isentropic Euler equations with periodic initial data. (English) Zbl 1316.35236 Arch. Ration. Mech. Anal. 216, No. 1, 221-259 (2015). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q31 35L65 76N10 PDFBibTeX XMLCite \textit{P. Qu} and \textit{Z. Xin}, Arch. Ration. Mech. Anal. 216, No. 1, 221--259 (2015; Zbl 1316.35236) Full Text: DOI
Love, E.; Rider, W. J. On the convergence of finite difference methods for PDE under temporal refinement. (English) Zbl 1416.65273 Comput. Math. Appl. 66, No. 1, 33-40 (2013). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{E. Love} and \textit{W. J. Rider}, Comput. Math. Appl. 66, No. 1, 33--40 (2013; Zbl 1416.65273) Full Text: DOI
Roberts, Joseph Steady and self-similar full Euler flow. (English) Zbl 1290.35153 J. Hyperbolic Differ. Equ. 10, No. 4, 799-840 (2013). MSC: 35L67 76N15 35Q31 PDFBibTeX XMLCite \textit{J. Roberts}, J. Hyperbolic Differ. Equ. 10, No. 4, 799--840 (2013; Zbl 1290.35153) Full Text: DOI arXiv
El Hajj, Ahmad; Monneau, Régis Uniqueness results for diagonal hyperbolic systems with large and monotone data. (English) Zbl 1284.35007 J. Hyperbolic Differ. Equ. 10, No. 3, 461-494 (2013). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35A02 35L45 35Q35 74H25 35K60 PDFBibTeX XMLCite \textit{A. El Hajj} and \textit{R. Monneau}, J. Hyperbolic Differ. Equ. 10, No. 3, 461--494 (2013; Zbl 1284.35007) Full Text: DOI
Bressan, Alberto Open questions in the theory of one dimensional hyperbolic conservation laws. (English) Zbl 1251.35045 Bressan, Alberto (ed.) et al., Nonlinear conservation laws and applications. Proceedings of the summer program, IMA, Minneapolis, MN, USA, July 13–31, 2009. New York, NY: Springer (ISBN 978-1-4419-9553-7; 978-1-4419-9554-4/ebook). The IMA Volumes in Mathematics and its Applications 153, 1-22 (2011). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 35-02 35-06 PDFBibTeX XMLCite \textit{A. Bressan}, IMA Vol. Math. Appl. 153, 1--22 (2011; Zbl 1251.35045) Full Text: DOI
Witteveen, Jeroen A. S. Second order front tracking for the Euler equations. (English) Zbl 1423.76357 J. Comput. Phys. 229, No. 7, 2719-2739 (2010). MSC: 76M25 35L65 35Q31 PDFBibTeX XMLCite \textit{J. A. S. Witteveen}, J. Comput. Phys. 229, No. 7, 2719--2739 (2010; Zbl 1423.76357) Full Text: DOI
Bianchini, Stefano; Spinolo, Laura V. The boundary Riemann solver coming from the real vanishing viscosity approximation. (English) Zbl 1171.35072 Arch. Ration. Mech. Anal. 191, No. 1, 1-96 (2009). Reviewer: V. D. Sharma (Mumbai) MSC: 35L65 35L67 35K65 PDFBibTeX XMLCite \textit{S. Bianchini} and \textit{L. V. Spinolo}, Arch. Ration. Mech. Anal. 191, No. 1, 1--96 (2009; Zbl 1171.35072) Full Text: DOI arXiv
Calvo, Daniela; Colombo, Rinaldo M.; Frid, Hermano \(L^{1}\) stability of spatially periodic solutions in relativistic gas dynamics. (English) Zbl 1168.35044 Commun. Math. Phys. 284, No. 2, 509-535 (2008). MSC: 35Q75 76Y05 76N15 35B10 35B35 35A35 PDFBibTeX XMLCite \textit{D. Calvo} et al., Commun. Math. Phys. 284, No. 2, 509--535 (2008; Zbl 1168.35044) Full Text: DOI
Glass, Olivier; LeFloch, Philippe G. Nonlinear hyperbolic systems: Nondegenerate flux, inner speed variation, and graph solutions. (English) Zbl 1124.35040 Arch. Ration. Mech. Anal. 185, No. 3, 409-480 (2007). Reviewer: Thomas Sonar (Braunschweig) MSC: 35L65 35L60 35L45 PDFBibTeX XMLCite \textit{O. Glass} and \textit{P. G. LeFloch}, Arch. Ration. Mech. Anal. 185, No. 3, 409--480 (2007; Zbl 1124.35040) Full Text: DOI arXiv
Witteveen, J. A. S.; Koren, B.; Bakker, P. G. An improved front tracking method for the Euler equations. (English) Zbl 1123.76055 J. Comput. Phys. 224, No. 2, 712-728 (2007). MSC: 76M25 35L65 35Q35 65M06 76L05 76N15 PDFBibTeX XMLCite \textit{J. A. S. Witteveen} et al., J. Comput. Phys. 224, No. 2, 712--728 (2007; Zbl 1123.76055) Full Text: DOI Link
Elling, Volker A Lax-Wendroff type theorem for unstructured quasi-uniform grids. (English) Zbl 1110.65060 Math. Comput. 76, No. 257, 251-272 (2007). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L05 65L50 34A34 65L20 PDFBibTeX XMLCite \textit{V. Elling}, Math. Comput. 76, No. 257, 251--272 (2007; Zbl 1110.65060) Full Text: DOI arXiv
LeFloch, Philippe G. Haar method, averaged matrix, wave cancellations, and \(L^{1}\) stability for hyperbolic systems. (English) Zbl 1116.35079 J. Hyperbolic Differ. Equ. 3, No. 4, 701-739 (2006). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35L45 35L65 76L05 74J40 PDFBibTeX XMLCite \textit{P. G. LeFloch}, J. Hyperbolic Differ. Equ. 3, No. 4, 701--739 (2006; Zbl 1116.35079) Full Text: DOI arXiv
Elling, Volker A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence. (English) Zbl 1114.35124 Math. Comput. 75, No. 256, 1721-1733 (2006). Reviewer: Stefan Balint (Timişoara) MSC: 35L65 PDFBibTeX XMLCite \textit{V. Elling}, Math. Comput. 75, No. 256, 1721--1733 (2006; Zbl 1114.35124) Full Text: DOI arXiv
Frid, Hermano; LeFloch, Philippe G. Uniqueness for multidimensional hyperbolic systems with commuting Jacobians. (English) Zbl 1103.35068 Arch. Ration. Mech. Anal. 182, No. 1, 25-47 (2006). MSC: 35L60 35L45 PDFBibTeX XMLCite \textit{H. Frid} and \textit{P. G. LeFloch}, Arch. Ration. Mech. Anal. 182, No. 1, 25--47 (2006; Zbl 1103.35068) Full Text: DOI
Dafermos, C. M. Hyperbolic systems of balance laws with weak dissipation. (English) Zbl 1107.35076 J. Hyperbolic Differ. Equ. 3, No. 3, 505-527 (2006). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35L45 35L65 PDFBibTeX XMLCite \textit{C. M. Dafermos}, J. Hyperbolic Differ. Equ. 3, No. 3, 505--527 (2006; Zbl 1107.35076) Full Text: DOI
Neves, Wladimir; Serre, Denis The incompleteness of the Born-Infeld model for nonlinear multi-D Maxwell’s equations. (English) Zbl 1100.35102 Q. Appl. Math. 63, No. 2, 343-367 (2005). Reviewer: Eric Sonnendrücker (Strasbourg) MSC: 35Q60 78A25 35L65 PDFBibTeX XMLCite \textit{W. Neves} and \textit{D. Serre}, Q. Appl. Math. 63, No. 2, 343--367 (2005; Zbl 1100.35102) Full Text: DOI
Gwiazda, Piotr; Świerczewska, Agnieszka Multivalued equations for granular avalanches. (English) Zbl 1074.35070 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 62, No. 5, 895-912 (2005). MSC: 35L65 35B35 35L45 74E20 76T25 PDFBibTeX XMLCite \textit{P. Gwiazda} and \textit{A. Świerczewska}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 62, No. 5, 895--912 (2005; Zbl 1074.35070) Full Text: DOI
Colombo, Rinaldo M. Wave front tracking in systems of conservation laws. (English) Zbl 1099.35063 Appl. Math., Praha 49, No. 6, 501-537 (2004). MSC: 35L65 35A35 35B35 35D05 PDFBibTeX XMLCite \textit{R. M. Colombo}, Appl. Math., Praha 49, No. 6, 501--537 (2004; Zbl 1099.35063) Full Text: DOI EuDML Link
LeFloch, Philippe G. Graph solutions of nonlinear hyperbolic systems. (English) Zbl 1071.35078 J. Hyperbolic Differ. Equ. 1, No. 4, 643-689 (2004). MSC: 35L60 35L65 76L05 74J40 35L67 35L45 PDFBibTeX XMLCite \textit{P. G. LeFloch}, J. Hyperbolic Differ. Equ. 1, No. 4, 643--689 (2004; Zbl 1071.35078) Full Text: DOI
Zhu, Changjiang; Zhao, Huijiang Well-posedness of the global entropy solution to the Cauchy problem of a hyperbolic conservation laws with relaxation. (English) Zbl 1049.35131 J. Math. Anal. Appl. 291, No. 2, 438-458 (2004). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 35L45 35D05 PDFBibTeX XMLCite \textit{C. Zhu} and \textit{H. Zhao}, J. Math. Anal. Appl. 291, No. 2, 438--458 (2004; Zbl 1049.35131) Full Text: DOI
Goatin, Paola One-sided estimates and uniqueness for hyperbolic systems of balance laws. (English) Zbl 1047.35093 Math. Models Methods Appl. Sci. 13, No. 4, 527-543 (2003). Reviewer: Marie Kopáčková (Praha) MSC: 35L60 35B45 35L45 35L65 PDFBibTeX XMLCite \textit{P. Goatin}, Math. Models Methods Appl. Sci. 13, No. 4, 527--543 (2003; Zbl 1047.35093) Full Text: DOI
Kong, De-Xing; Yang, T. A note on “Well-posedness theory for hyperbolic conservation laws”. (English) Zbl 1073.35159 Appl. Math. Lett. 16, No. 2, 143-146 (2003). MSC: 35L65 35B30 PDFBibTeX XMLCite \textit{D.-X. Kong} and \textit{T. Yang}, Appl. Math. Lett. 16, No. 2, 143--146 (2003; Zbl 1073.35159) Full Text: DOI
Yang, Tong; Zhao, Huijiang; Zhu, Changjiang BV estimates of Lax-Friedrichs’ scheme for a class of nonlinear hyperbolic conservation laws. (English) Zbl 1195.35209 Proc. Am. Math. Soc. 131, No. 4, 1257-1266 (2003). MSC: 35L60 35L65 65N12 PDFBibTeX XMLCite \textit{T. Yang} et al., Proc. Am. Math. Soc. 131, No. 4, 1257--1266 (2003; Zbl 1195.35209) Full Text: DOI
Nieto, J.; Soler, J.; Poupaud, F. About uniqueness of weak solutions to first order quasi-linear equations. (English) Zbl 1027.35072 Math. Models Methods Appl. Sci. 12, No. 11, 1599-1615 (2002). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 35A35 35L45 PDFBibTeX XMLCite \textit{J. Nieto} et al., Math. Models Methods Appl. Sci. 12, No. 11, 1599--1615 (2002; Zbl 1027.35072) Full Text: DOI
Baiti, Paolo; LeFloch, Philippe G.; Piccoli, Benedetto Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems. (English) Zbl 0987.35101 J. Differ. Equations 172, No. 1, 59-82 (2001). Reviewer: R.Luca (Iaşi) MSC: 35L45 35L65 35A05 PDFBibTeX XMLCite \textit{P. Baiti} et al., J. Differ. Equations 172, No. 1, 59--82 (2001; Zbl 0987.35101) Full Text: DOI
Chen, Gui-Qiang; Frid, Hermano Uniqueness and asymptotic stability of Riemann solutions for the compressible Euler equations. (English) Zbl 0958.35094 Trans. Am. Math. Soc. 353, No. 3, 1103-1117 (2001). MSC: 35Q05 35Q35 35B35 35B40 76N15 35L65 PDFBibTeX XMLCite \textit{G.-Q. Chen} and \textit{H. Frid}, Trans. Am. Math. Soc. 353, No. 3, 1103--1117 (2001; Zbl 0958.35094) Full Text: DOI
Liu, Tai-Ping; Yang, Tong Well-posedness theory for hyperbolic conservation laws. (English) Zbl 1034.35073 Commun. Pure Appl. Math. 52, No. 12, 1553-1586 (1999). MSC: 35L65 PDFBibTeX XMLCite \textit{T.-P. Liu} and \textit{T. Yang}, Commun. Pure Appl. Math. 52, No. 12, 1553--1586 (1999; Zbl 1034.35073) Full Text: DOI
Bressan, Alberto; Goatin, Paola Oleinik type estimates and uniqueness for \(n \times n\) conservation laws. (English) Zbl 0990.35095 J. Differ. Equations 156, No. 1, 26-49 (1999). Reviewer: R.Luca (Iaşi) MSC: 35L65 35B45 35L45 PDFBibTeX XMLCite \textit{A. Bressan} and \textit{P. Goatin}, J. Differ. Equations 156, No. 1, 26--49 (1999; Zbl 0990.35095) Full Text: DOI
Liu, Tai-Ping; Yang, Tong \(L_1\) stability for \(2\times 2\) systems of hyperbolic conservation laws. (English) Zbl 0924.35083 J. Am. Math. Soc. 12, No. 3, 729-774 (1999). Reviewer: A.Doktor (Praha) MSC: 35L67 35L45 76L05 35L65 PDFBibTeX XMLCite \textit{T.-P. Liu} and \textit{T. Yang}, J. Am. Math. Soc. 12, No. 3, 729--774 (1999; Zbl 0924.35083) Full Text: DOI
Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik An unconditionally stable method for the Euler equations. (English) Zbl 0922.76251 J. Comput. Phys. 150, No. 1, 76-96 (1999). MSC: 76M20 76N10 76L05 PDFBibTeX XMLCite \textit{H. Holden} et al., J. Comput. Phys. 150, No. 1, 76--96 (1999; Zbl 0922.76251) Full Text: DOI Link