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Journal articles on the topic 'Hyperbolic balance laws'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Dafermos, Constantine. "Hyperbolic balance laws with relaxation." Discrete and Continuous Dynamical Systems 36, no. 8 (2016): 4271–85. http://dx.doi.org/10.3934/dcds.2016.36.4271.

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2

Miroshnikov, Alexey, and Konstantina Trivisa. "Stability and convergence of relaxation schemes to hyperbolic balance laws via a wave operator." Journal of Hyperbolic Differential Equations 12, no. 01 (2015): 189–219. http://dx.doi.org/10.1142/s0219891615500058.

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This paper deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before the formation of shocks, provided that we are within the framework of the compensated compactness method. Our analysis treats systems of hyperbolic balance laws with source terms satisfying a special mechanism which induces weak dissipation in the spirit of Dafermos [Hyperbolic systems of balance laws with weak dissipation, J. Hyp. Diff. Equations 3 (2006) 505–5

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3

DAFERMOS, CONSTANTINE M. "N-WAVES IN HYPERBOLIC BALANCE LAWS." Journal of Hyperbolic Differential Equations 09, no. 02 (2012): 339–54. http://dx.doi.org/10.1142/s0219891612500117.

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It is shown that, as time tends to infinity, solutions to the Cauchy problem for a class of genuinely nonlinear scalar balance laws attain N-wave profiles, when the initial data have compact support, or saw-toothed profiles, when the initial data are periodic. The amplitude and length of these waves results from the synergy between flux and source.

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4

DAFERMOS, CONSTANTINE M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION II." Journal of Hyperbolic Differential Equations 10, no. 01 (2013): 173–79. http://dx.doi.org/10.1142/s0219891613500070.

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By extending the analysis in [C. M. Dafermos, Hyperbolic systems of balance laws with weak dissipation, J. Hyperbolic Differ. Equ.3 (2006) 505–527], this note constructs global BV solutions to the Cauchy problem for strictly hyperbolic systems of balance laws endowed with a convex entropy, under the assumption that the entropy production is positive definite.

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5

Abgrall, Rémi, Mauro Garavello, Mária Lukáčová-Medvid’ová, and Konstantina Trivisa. "Hyperbolic Balance Laws: Interplay between Scales and Randomness." Oberwolfach Reports 21, no. 1 (2024): 567–656. http://dx.doi.org/10.4171/owr/2024/10.

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Hyperbolic balance laws are fundamental in the mathematical modeling of transport-dominated processes in natural, socio-economic and engineering sciences. The aim of the workshop was to discuss open questions in the area of nonlinear hyperbolic conservation and balance laws. We have focused on a delicate interplay between scale hierarchies and random/stochastic effects and discuss them from analytical, numerical and modeling point of view. This leads to questions of admissibility criteria connecting to ill-posedness of weak entropy solutions, hyperbolic problems with non-local terms, mean fiel

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Abgrall, Rémi, Mauro Garavello, Mária Lukáčová-Medvid’ová, and Konstantina Trivisa. "Hyperbolic Balance Laws: modeling, analysis, and numerics." Oberwolfach Reports 18, no. 1 (2022): 589–661. http://dx.doi.org/10.4171/owr/2021/11.

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7

COLOMBO, RINALDO M., and ANDREA CORLI. "ON A CLASS OF HYPERBOLIC BALANCE LAWS." Journal of Hyperbolic Differential Equations 01, no. 04 (2004): 725–45. http://dx.doi.org/10.1142/s0219891604000317.

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Consider an n×n system of hyperbolic balance laws with coinciding shock and rarefaction curves. This note proves the well-posedness in the large of this system, provided there exists a domain that is invariant both with respect to the homogeneous conservation law and to the ordinary differential system generated by the right-hand side. No "non-resonance" hypothesis is assumed.

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8

Christoforou, Cleopatra, and Konstantina Trivisa. "Sharp decay estimates for hyperbolic balance laws." Journal of Differential Equations 247, no. 2 (2009): 401–23. http://dx.doi.org/10.1016/j.jde.2009.03.013.

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9

Falle, Samuel A., and Robin J. Williams. "Shock Structures Described by Hyperbolic Balance Laws." SIAM Journal on Applied Mathematics 79, no. 1 (2019): 459–76. http://dx.doi.org/10.1137/18m1216390.

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10

Sever, Michael. "Extensions of hyperbolic systems of balance laws." Continuum Mechanics and Thermodynamics 17, no. 6 (2006): 453–68. http://dx.doi.org/10.1007/s00161-006-0011-z.

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11

Gugat, Martin. "New Lyapunov functions for systems with source terms." Control and Cybernetics 53, no. 1 (2024): 163–87. https://doi.org/10.2478/candc-2024-008.

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Abstract Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic functions and study the advantages in the analysis of 2 × 2 systems of balance laws. We present cases connected with the study of the limit of stabilizability, where the new weights provide Lyapunov functions that show exponential stability for a larger set of problem parameters than classical exponential weights. Moreover, we show that sufficiently la

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12

Gugat, Martin. "New Lyapunov functions for systems with source terms." Control and Cybernetics 53, no. 1 (2025): 163–87. https://doi.org/10.2478/candc-2024-0008.

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Abstract Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic functions and study the advantages in the analysis of 2 × 2 systems of balance laws. We present cases connected with the study of the limit of stabilizability, where the new weights provide Lyapunov functions that show exponential stability for a larger set of problem parameters than classical exponential weights. Moreover, we show that sufficiently la

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13

DAFERMOS, C. M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION." Journal of Hyperbolic Differential Equations 03, no. 03 (2006): 505–27. http://dx.doi.org/10.1142/s0219891606000884.

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Global BV solutions are constructed to the Cauchy problem for strictly hyperbolic systems of balance laws endowed with a rich family of entropies and source that is merely weakly dissipative, of the type induced by relaxation mechanisms.

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14

Abreu, Eduardo, John Perez, and Arthur Santo. "Lagrangian-Eulerian approximation methods for balance laws and hyperbolic conservation laws." Revista UIS Ingenierías 13, no. 1 (2018): 191–200. http://dx.doi.org/10.18273/revuin.v17n1-2018018.

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15

Dafermos, Constantine M. "Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws." Ricerche di Matematica 67, no. 2 (2017): 755–64. http://dx.doi.org/10.1007/s11587-017-0338-8.

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16

Colombo, Rinaldo M., and Graziano Guerra. "Hyperbolic Balance Laws with a Non Local Source." Communications in Partial Differential Equations 32, no. 12 (2007): 1917–39. http://dx.doi.org/10.1080/03605300701318849.

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17

Yong, Wen-An. "Entropy and Global Existence for Hyperbolic Balance Laws." Archive for Rational Mechanics and Analysis 172, no. 2 (2004): 247–66. http://dx.doi.org/10.1007/s00205-003-0304-3.

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18

Christoforou, Cleopatra, and Konstantina Trivisa. "Decay of Positive Waves of Hyperbolic Balance Laws." Acta Mathematica Scientia 32, no. 1 (2012): 352–66. http://dx.doi.org/10.1016/s0252-9602(12)60022-8.

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19

Ehrt, Julia. "Parametrizations of sub-attractors in hyperbolic balance laws." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 3 (2012): 563–83. http://dx.doi.org/10.1017/s030821051000096x.

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We investigate the properties of the global attractor of hyperbolic balance laws on the circle, given byut + f(u)x = g(u).The new tool of sub-attractors is introduced. They contain all solutions on the global attractor up to a given number of zeros. The paper proves finite dimensionality of all sub-attractors, provides a full parametrization of all sub-attractors and derives a system of ordinary differential equations for the embedding parameters that describe the full partial differential equation dynamics on the sub-attractor.

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20

Christoforou, Cleopatra C. "Hyperbolic systems of balance laws via vanishing viscosity." Journal of Differential Equations 221, no. 2 (2006): 470–541. http://dx.doi.org/10.1016/j.jde.2005.03.010.

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21

Miroshnikov, Alexey, and Konstantina Trivisa. "Relative entropy in hyperbolic relaxation for balance laws." Communications in Mathematical Sciences 12, no. 6 (2014): 1017–43. http://dx.doi.org/10.4310/cms.2014.v12.n6.a2.

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22

Dafermos, Constantine M. "Hyperbolic systems of balance laws with stiff source." Journal of Differential Equations 375 (December 2023): 250–76. http://dx.doi.org/10.1016/j.jde.2023.08.003.

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23

Härterich, Jörg. "Heteroclinic orbits between rotating waves in hyperbolic balance laws." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 3 (1999): 519–38. http://dx.doi.org/10.1017/s0308210500021491.

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We deal with the large-time behaviour of scalar hyperbolic conservation laws with source termswhich are often called hyperbolic balance laws. Fan and Hale have proved existence of a global attractorfor this equation withx∈S1.consists of spatially homogeneous equilibria, a large number of rotating waves and of heteroclinic orbits between these objects. In this paper, we solve the connection problem and show which equilibria and rotating waves are connected by a heteroclinic orbit. Apart from existence results, our approach via generalized characteristics also gives geometric information about t

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24

Zeng, Yanni. "Global existence theory for general hyperbolic-parabolic balance laws with application." Journal of Hyperbolic Differential Equations 14, no. 02 (2017): 359–91. http://dx.doi.org/10.1142/s0219891617500126.

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We study a general system of hyperbolic-parabolic balance laws in [Formula: see text] space dimensions ([Formula: see text]). The system has rank deficient viscosity matrices and a lower order term whose Jacobian matrix is rank deficient as well. We consider the Cauchy problem when initial data are small perturbations of a constant equilibrium state. Under a set of reasonable assumptions including Kawashima–Shizuta condition, we establish the existence of solution global in time via energy method. The proposed assumptions are sufficiently general for applications to physical models such as ele

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25

Ancona, Fabio, Laura Caravenna, and Andrea Marson. "On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function." Journal of Hyperbolic Differential Equations 16, no. 02 (2019): 333–78. http://dx.doi.org/10.1142/s0219891619500139.

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The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one

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26

Zeng, Yanni. "Lp time asymptotic decay for general hyperbolic–parabolic balance laws with applications." Journal of Hyperbolic Differential Equations 16, no. 04 (2019): 663–700. http://dx.doi.org/10.1142/s021989161950022x.

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We study the time asymptotic decay of solutions for a general system of hyperbolic–parabolic balance laws in one space dimension. The system has a physical viscosity matrix and a lower-order term for relaxation, damping or chemical reaction. The viscosity matrix and the Jacobian matrix of the lower-order term are rank deficient. For Cauchy problem around a constant equilibrium state, existence of solution global in time has been established recently under a set of reasonable assumptions. In this paper, we obtain optimal [Formula: see text] decay rates for [Formula: see text]. Our result is gen

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27

M. Colombo, Rinaldo, and Graziano Guerra. "Hyperbolic balance laws with a dissipative non local source." Communications on Pure & Applied Analysis 7, no. 5 (2008): 1077–90. http://dx.doi.org/10.3934/cpaa.2008.7.1077.

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28

Yong, Wen-An. "Boundary stabilization of hyperbolic balance laws with characteristic boundaries." Automatica 101 (March 2019): 252–57. http://dx.doi.org/10.1016/j.automatica.2018.12.003.

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29

Natalini, R., C. Sinestrari, and A. Tesei. "Incomplete blowup of solutions of quasilinear hyperbolic balance laws." Archive for Rational Mechanics and Analysis 135, no. 3 (1996): 259–96. http://dx.doi.org/10.1007/bf02198141.

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30

Shao, Zhi-Qiang. "Shock reflection for a system of hyperbolic balance laws." Journal of Mathematical Analysis and Applications 343, no. 2 (2008): 1131–53. http://dx.doi.org/10.1016/j.jmaa.2008.02.021.

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31

Romeo, Maurizio. "Hyperbolic system of balance laws modeling dissipative ionic crystals." Zeitschrift für angewandte Mathematik und Physik 58, no. 4 (2006): 697–714. http://dx.doi.org/10.1007/s00033-006-6071-x.

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32

Yu, Hongjun. "Large time behavior of solutions for hyperbolic balance laws." Journal of Differential Equations 261, no. 9 (2016): 4789–824. http://dx.doi.org/10.1016/j.jde.2016.07.016.

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33

Sinestrari, Carlo. "Instability of Discontinuous Traveling Waves for Hyperbolic Balance Laws." Journal of Differential Equations 134, no. 2 (1997): 269–85. http://dx.doi.org/10.1006/jdeq.1996.3223.

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34

Mascia, C. "Travelling wave solutions for a balance law." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 3 (1997): 567–93. http://dx.doi.org/10.1017/s0308210500029917.

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We study entropy travelling wave solutions for first-order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex fluxes and source terms with simple isolated zeros.

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35

Hong, John Meng-Kai, and Reyna Marsya Quita. "Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times." Tamkang Journal of Mathematics 48, no. 1 (2017): 73–94. http://dx.doi.org/10.5556/j.tkjm.48.2017.2274.

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In this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ hyperbolic system of balance laws with $global$ source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized approximate solu

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36

CHRISTOFOROU, CLEOPATRA. "SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH MEMORY." Journal of Hyperbolic Differential Equations 04, no. 03 (2007): 435–78. http://dx.doi.org/10.1142/s0219891607001215.

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Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly stable in L1with respect to the initial data and converge to equilibrium as t → ∞. The motivation to study these systems is the observation that conservations laws with fading memory can be written in such

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37

Schmitt, Johann M., and Stefan Ulbrich. "Optimal Boundary Control of Hyperbolic Balance Laws with State Constraints." SIAM Journal on Control and Optimization 59, no. 2 (2021): 1341–69. http://dx.doi.org/10.1137/19m129797x.

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38

Diagne, Ababacar, Georges Bastin, and Jean-Michel Coron. "Lyapunov exponential stability of linear hyperbolic systems of balance laws." IFAC Proceedings Volumes 44, no. 1 (2011): 13320–25. http://dx.doi.org/10.3182/20110828-6-it-1002.01506.

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39

Gerster, Stephan, and Michael Herty. "Discretized feedback control for systems of linearized hyperbolic balance laws." Mathematical Control & Related Fields 9, no. 3 (2019): 517–39. http://dx.doi.org/10.3934/mcrf.2019024.

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40

Tang, Ying, Christophe Prieur, and Antoine Girard. "Singular Perturbation Approximation of Linear Hyperbolic Systems of Balance Laws." IEEE Transactions on Automatic Control 61, no. 10 (2016): 3031–37. http://dx.doi.org/10.1109/tac.2015.2499444.

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41

Kawashima, S., and W. A. Yong. "Dissipative Structure and Entropy for Hyperbolic Systems of Balance Laws." Archive for Rational Mechanics and Analysis 174, no. 3 (2004): 345–64. http://dx.doi.org/10.1007/s00205-004-0330-9.

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42

Dafermos, Constantine M. "BV solutions for hyperbolic systems of balance laws with relaxation." Journal of Differential Equations 255, no. 8 (2013): 2521–33. http://dx.doi.org/10.1016/j.jde.2013.07.002.

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43

Kröker, I., and C. Rohde. "Finite volume schemes for hyperbolic balance laws with multiplicative noise." Applied Numerical Mathematics 62, no. 4 (2012): 441–56. http://dx.doi.org/10.1016/j.apnum.2011.01.011.

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44

Dafermos, Constantine M. "Periodic BV solutions of hyperbolic balance laws with dissipative source." Journal of Mathematical Analysis and Applications 428, no. 1 (2015): 405–13. http://dx.doi.org/10.1016/j.jmaa.2015.03.026.

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45

Ben-Artzi, Matania, and Jiequan Li. "Consistency of finite volume approximations to nonlinear hyperbolic balance laws." Mathematics of Computation 90, no. 327 (2020): 141–69. http://dx.doi.org/10.1090/mcom/3569.

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46

Ben-Artzi, Matania, and Jiequan Li. "Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem." Numerische Mathematik 106, no. 3 (2007): 369–425. http://dx.doi.org/10.1007/s00211-007-0069-y.

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47

Tang, Pingfan, and Ya-Guang Wang. "Shock waves for the hyperbolic balance laws with discontinuous sources." Mathematical Methods in the Applied Sciences 37, no. 14 (2013): 2029–64. http://dx.doi.org/10.1002/mma.2952.

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48

GODVIK, MARTE, and HARALD HANCHE-OLSEN. "EXISTENCE OF SOLUTIONS FOR THE AW–RASCLE TRAFFIC FLOW MODEL WITH VACUUM." Journal of Hyperbolic Differential Equations 05, no. 01 (2008): 45–63. http://dx.doi.org/10.1142/s0219891608001428.

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In this paper, the macroscopic model for traffic flow proposed by Aw and Rascle in 2000 is considered. The model is a 2 × 2 system of hyperbolic conservation laws, or, when the model includes a relaxation term, a 2 × 2 system of hyperbolic balance laws. The main difficulty is the presence of vacuum, which makes control of the total variation of the conservative variables impossible. We allow vacuum to appear and prove the existence of a weak entropy solution to the Cauchy problem.

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49

Jin, Shi, Dongbin Xiu, and Xueyu Zhu. "A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs." Journal of Scientific Computing 67, no. 3 (2015): 1198–218. http://dx.doi.org/10.1007/s10915-015-0124-2.

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50

GOATIN, PAOLA. "ONE-SIDED ESTIMATES AND UNIQUENESS FOR HYPERBOLIC SYSTEMS OF BALANCE LAWS." Mathematical Models and Methods in Applied Sciences 13, no. 04 (2003): 527–43. http://dx.doi.org/10.1142/s0218202503002611.

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Uniqueness of solutions of genuinely nonlinear n × n strictly hyperbolic systems of balance laws is established moving from Oleïnik-type decay estimates. As middle step, the result relies on the fulfillment of a condition which controls the local oscillation of the solution in a forward neighborhood of each point in the t–x plane.

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