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Relevant bibliographies by topics / Hyperbolic balance laws

Academic literature on the topic 'Hyperbolic balance laws'

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Published: 6 September 2023

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Journal articles on the topic "Hyperbolic balance laws"

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

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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 (March 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) 505–527.], as well as hyperbolic balance laws with more general source terms. The rate of convergence of the relaxation system to a solution of the balance laws in the smooth regime is established. Our work follows in spirit the analysis presented by [Ch. Arvanitis, Ch. Makridakis and A. E. Tzavaras, Stability and convergence of a class of finite element schemes for hyperbolic conservation laws, SIAM J. Numer. Anal. 42(4) (2004) 1357–1393]; [S. Jin and X. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995) 235–277] for systems of hyperbolic conservation laws without source terms.

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DAFERMOS, CONSTANTINE M. "N-WAVES IN HYPERBOLIC BALANCE LAWS." Journal of Hyperbolic Differential Equations 09, no. 02 (June 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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DAFERMOS, CONSTANTINE M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION II." Journal of Hyperbolic Differential Equations 10, no. 01 (March 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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Abgrall, Rémi, Mauro Garavello, Mária Lukáčová-Medvid’ová, and Konstantina Trivisa. "Hyperbolic Balance Laws: modeling, analysis, and numerics." Oberwolfach Reports 18, no. 1 (March 14, 2022): 589–661. http://dx.doi.org/10.4171/owr/2021/11.

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COLOMBO, RINALDO M., and ANDREA CORLI. "ON A CLASS OF HYPERBOLIC BALANCE LAWS." Journal of Hyperbolic Differential Equations 01, no. 04 (December 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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Christoforou, Cleopatra, and Konstantina Trivisa. "Sharp decay estimates for hyperbolic balance laws." Journal of Differential Equations 247, no. 2 (July 2009): 401–23. http://dx.doi.org/10.1016/j.jde.2009.03.013.

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

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Sever, Michael. "Extensions of hyperbolic systems of balance laws." Continuum Mechanics and Thermodynamics 17, no. 6 (March 9, 2006): 453–68. http://dx.doi.org/10.1007/s00161-006-0011-z.

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DAFERMOS, C. M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION." Journal of Hyperbolic Differential Equations 03, no. 03 (September 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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Dissertations / Theses on the topic "Hyperbolic balance laws"

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Sen, Chhanda. "Entropy stable numerical schemes for hyperbolic balance laws." Thesis, IIT Delhi, 2019. http://eprint.iitd.ac.in:80//handle/2074/8135.

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Ehrt, Julia [Verfasser]. "Cascades of heteroclinic connections in hyperbolic balance laws / Julia Ehrt." Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V, 2010. http://d-nb.info/1042738963/34.

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Ehrt, Julia [Verfasser]. "Cascades of heteroclinic connections in hyperbolic balance laws / Julia Michael Ehrt." Berlin : Freie Universität Berlin, 2010. http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000015791-0.

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Weldegiyorgis, Gediyon Yemane. "Numerical stabilization with boundary controls for hyperbolic systems of balance laws." Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60870.

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In this dissertation, boundary stabilization of a linear hyperbolic system of balance laws is considered. Of particular interest is the numerical boundary stabilization of such systems. An analytical stability analysis of the system will be presented as a preamble. A discussion of the application of the analysis on speci c examples: telegrapher equations, isentropic Euler equations, Saint-Venant equations and Saint-Venant-Exner equations is also presented. The rst order explicit upwind scheme is applied for the spatial discretization. For the temporal discretization a splitting technique is applied. A discrete 𝕃 ²−Lyapunov function is employed to investigate conditions for the stability of the system. A numerical analysis is undertaken and convergence of the solution to its equilibrium is proved. Further a numerical implementation is presented. The numerical computations also demonstrate the stability of the numerical scheme with parameters chosen to satisfy the stability requirements.
Dissertation (MSc)--University of Pretoria, 2016.
Mathematics and Applied Mathematics
MSc
Unrestricted

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ROSSI, ELENA. "Balance Laws: Non Local Mixed Systems and IBVPs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/103090.

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Scalar hyperbolic balance laws in several space dimensions play a central role in this thesis. First, we deal with a new class of mixed parabolic-hyperbolic systems on all R^n: we obtain the basic well-posedness theorems, devise an ad hoc numerical algorithm, prove its convergence and investigate the qualitative properties of the solutions. The extension of these results to bounded domains requires a deep understanding of the initial boundary value problem (IBVP) for hyperbolic balance laws. The last part of the thesis provides rigorous estimates on the solution to this IBVP, under precise regularity assumptions. In Chapter 1 we introduce a predator-prey model. A non local and non linear balance law is coupled with a parabolic equation: the former describes the evolution of the predator density, the latter that of prey. The two equations are coupled both through the convective part of the balance law and the source terms. The drift term is a non local function of the prey density. This allows the movement of predators to be directed towards the regions where the concentration of prey is higher. We prove the well-posedness of the system, hence the existence and uniqueness of solution, the continuous dependence from the initial data and various stability estimates. In Chapter 2 we devise an algorithm to compute approximate solutions to the mixed system introduced above. The balance law is solved numerically by a Lax-Friedrichs type method via dimensional splitting, while the parabolic equation is approximated through explicit finite-differences. Both source terms are integrated by means of a second order Runge-Kutta scheme. The key result in Chapter 2 is the convergence of this algorithm. The proof relies on a careful tuning between the parabolic and the hyperbolic methods and exploits the non local nature of the convective part in the balance law. This algorithm has been implemented in a series of Python scripts. Using them, we obtain information about the possible order of convergence and we investigate the qualitative properties of the solutions. Moreover, we observe the formation of a striking pattern: while prey diffuse, predators accumulate on the vertices of a regular lattice. The analytic study of the system above is on all R^n. However, both possible biological applications and numerical integrations suggest that the boundary plays a relevant role. With the aim of studying the mixed hyperbolic-parabolic system in a bounded domain, we noticed that for balance laws known results lack some of the estimates necessary to deal with the coupling. In Chapter 3 we then focus on the IBVP for a general balance law in a bounded domain. We prove the well-posedness of this problem, first with homogeneous boundary condition, exploiting the vanishing viscosity technique and the doubling of variables method, then for the non homogeneous case, mainly thanks to elliptic techniques. We pay particular attention to the regularity assumptions and provide rigorous estimates on the solution.

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Mantri, Yogiraj Verfasser], Sebastian [Akademischer Betreuer] Noelle, and Michael [Akademischer Betreuer] [Herty. "Computing near-equilibrium solutions for hyperbolic balance laws on networks / Yogiraj Mantri ; Sebastian Noelle, Michael Herty." Aachen : Universitätsbibliothek der RWTH Aachen, 2021. http://d-nb.info/1228433038/34.

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Gerster, Stephan [Verfasser], Michael [Akademischer Betreuer] Herty, Martin [Akademischer Betreuer] Frank, and Simone [Akademischer Betreuer] Göttlich. "Stabilization and uncertainty quantification for systems of hyperbolic balance laws / Stephan Gerster ; Michael Herty, Martin Frank, Simone Göttlich." Aachen : Universitätsbibliothek der RWTH Aachen, 2020. http://d-nb.info/1216638136/34.

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Schmitt, Johann Michael [Verfasser]. "Optimal Control of Initial-Boundary Value Problems for Hyperbolic Balance Laws with Switching Controls and State Constraints / Johann Michael Schmitt." München : Verlag Dr. Hut, 2019. http://d-nb.info/1188516450/34.

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Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.

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Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin des années $1960$, son assimilation dans la théorie du contrôle s'est rapidement développée et est devenue un outil majeur pour l'analyse et la synthèse de la commande des systèmes. Les perturbations singulières sont une façon de négliger la transition rapide, en la considérant dans une échelle de temps rapide séparée. Ce travail de thèse se concentre sur les systèmes hyperboliques linéaires avec des échelles de temps multiples modélisées par un petit paramètre de perturbation. Tout d'abord, nous étudions une classe de systèmes hyperboliques linéaires singulièrement perturbés. Comme le système contient deux échelles de temps, en mettant le paramètre de la perturbation à zéro, deux sous-systèmes, le système réduit et la couche limite, sont formellement calculés. La stabilité du système complet de lois de conservation implique la stabilité des deux sous-systèmes. En revanche un contre-exemple est utilisé pour illustrer que la stabilité des deux sous-systèmes ne suffit pas à garantir la stabilité du système complet. Cela montre une grande différence avec ce qui est bien connu pour les systèmes linéaires en dimension finie modélisés par des équations aux dérivées ordinaires (EDO). De plus, sous certaines conditions, l'approximation de Tikhonov est obtenue pour tels systèmes par la méthode de Lyapunov. Plus précisément, la solution de la dynamique lente du système complet est approchée par la solution du système réduit lorsque le paramètre de la perturbation est suffisamment petit. Deuxièmement, le théorème de Tikhonov est établi pour les systèmes hyperboliques linéaires singulièrement perturbés de lois d'équilibre où les vitesses de transport et les termes sources sont à la fois dépendant du paramètre de la perturbation ainsi que les conditions aux bords. Sous des hypothèses sur la continuité de ces termes et sous la condition de la stabilité, l'estimation de l'erreur entre la dynamique lente du système complet et le système réduit est obtenue en fonction de l'ordre du paramètre de la perturbation. Troisièmement, nous considérons des systèmes EDO-EDP couplés singulièrement perturbés. La stabilité des deux sous-systèmes implique la stabilité du système complet où le paramètre de la perturbation est introduit dans la dynamique de l'EDP. D'autre part, cela n'est pas valable pour le système où le paramètre de la perturbation est présent dans l'EDO. Le théorème Tikhonov pour ces systèmes EDO-EDP couplés est prouvé par la technique de Lyapunov. Enfin, la synthèse de la commande aux bords est abordée en exploitant la méthode des perturbations singulières. Le système réduit converge en temps fini. La synthèse du contrôle aux bords est mise en œuvre pour deux applications différentes afin d'illustrer les résultats principaux de ce travail
Systems modeled by partial differential equations (PDEs) with infinite dimensional dynamics are relevant for a wide range of physical networks. The control and stability analysis of such systems become a challenge area. Singularly perturbed systems, containing multiple time scales, often occur naturally in physical systems due to the presence of small parasitic parameters, typically small time constants, masses, inductances, moments of inertia. Singular perturbation was introduced in control engineering in late $1960$s, its assimilation in control theory has rapidly developed and has become a tool for analysis and design of control systems. Singular perturbation is a way of neglecting the fast transition and considering them in a separate fast time scale. The present thesis is concerned with a class of linear hyperbolic systems with multiple time scales modeled by a small perturbation parameter. Firstly we study a class of singularly perturbed linear hyperbolic systems of conservation laws. Since the system contains two time scales, by setting the perturbation parameter to zero, the two subsystems, namely the reduced subsystem and the boundary-layer subsystem, are formally computed. The stability of the full system implies the stability of both subsystems. However a counterexample is used to illustrate that the stability of the two subsystems is not enough to guarantee the full system's stability. This shows a major difference with what is well known for linear finite dimensional systems. Moreover, under certain conditions, the Tikhonov approximation for such system is achieved by Lyapunov method. Precisely, the solution of the slow dynamics of the full system is approximated by the solution of the reduced subsystem for sufficiently small perturbation parameter. Secondly the Tikhonov theorem is established for singularly perturbed linear hyperbolic systems of balance laws where the transport velocities and source terms are both dependent on the perturbation parameter as well as the boundary conditions. Under the assumptions on the continuity for such terms and under the stability condition, the estimate of the error between the slow dynamics of the full system and the reduced subsystem is the order of the perturbation parameter. Thirdly, we consider singularly perturbed coupled ordinary differential equation ODE-PDE systems. The stability of both subsystems implies that of the full system where the perturbation parameter is introduced into the dynamics of the PDE system. On the other hand, this is not true for system where the perturbation parameter is presented to the ODE. The Tikhonov theorem for such coupled ODE-PDE systems is proved by Lyapunov technique. Finally, the boundary control synthesis is achieved based on singular perturbation method. The reduced subsystem is convergent in finite time. Boundary control design to different applications are used to illustrate the main results of this work

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MARCELLINI, FRANCESCA. "Conservation laws in gas dynamics and traffic flow." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2009. http://hdl.handle.net/10281/7487.

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This PhD thesis is concerned with applications of nonlinear systems of conservation laws to gas dynamics and traffic flow modeling. The first part is devoted to the analytical description of a fluid flowing in a tube with varying cross section. We study the 2x2 model of the p-system and than, we extend the properties to the full 3x3 Euler system. We also consider a general nxn strictly hyperbolic system of balance laws; we study the Cauchy problem for this system and we apply this result to the fluid flow in a pipe wiyh varying section. Concerning traffic flow, we introduce a new macroscopic model, based on a non-smooth 2x2 system of conservation laws. We study the Riemann problem for this system and the qualitative properties of its solutions that are relevant from the point of view of traffic.

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Books on the topic "Hyperbolic balance laws"

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Bressan, Alberto, Denis Serre, Mark Williams, and Kevin Zumbrun. Hyperbolic Systems of Balance Laws. Edited by Pierangelo Marcati. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72187-1.

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Bartecki, Krzysztof. Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27501-7.

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Albi, Giacomo, Walter Boscheri, and Mattia Zanella, eds. Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-29875-2.

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1956-, Bressan Alberto, Marcati P. A, and Centro internazionale matematico estivo, eds. Hyperbolic systems of balance laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003. Berlin: Springer, 2007.

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Bartecki, Krzysztof. Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws. Springer, 2018.

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Bartecki, Krzysztof. Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws. Springer, 2015.

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Bartecki, Krzysztof. Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws. Springer London, Limited, 2016.

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Bressan, Alberto, Denis Serre, Kevin Zumbrun, Mark Williams, and Pierangelo Marcati. Hyperbolic Systems of Balance Laws: Lectures Given at the C. I. M. E. Summer School Held in Cetraro, Italy, July 14-21 2003. Springer London, Limited, 2007.

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Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: And Well-Balanced Schemes for Sources (Frontiers in Mathematics). Birkhäuser Basel, 2005.

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Book chapters on the topic "Hyperbolic balance laws"

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Bartecki, Krzysztof. "Hyperbolic Systems of Balance Laws." In Studies in Systems, Decision and Control, 7–22. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-27501-7_2.

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Dafermos, Constantine M. "Hyperbolic Systems of Balance Laws." In Grundlehren der mathematischen Wissenschaften, 53–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49451-6_3.

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Dafermos, Constantine M. "Hyperbolic Systems of Balance Laws." In Grundlehren der mathematischen Wissenschaften, 37–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-22019-1_3.

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Dafermos, Constantine M. "Hyperbolic Systems of Balance Laws." In Grundlehren der mathematischen Wissenschaften, 53–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04048-1_3.

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Bastin, Georges, and Jean-Michel Coron. "Hyperbolic Systems of Balance Laws." In Stability and Boundary Stabilization of 1-D Hyperbolic Systems, 1–54. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32062-5_1.

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Russo, Giovanni. "Central Schemes for Balance Laws." In Hyperbolic Problems: Theory, Numerics, Applications, 821–29. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8372-6_35.

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Meister, Andreas, and Jens Struckmeier. "Central Schemes and Systems of Balance Laws." In Hyperbolic Partial Differential Equations, 59–114. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80227-9_2.

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Christoforou, Cleopatra. "On Hyperbolic Balance Laws and Applications." In Innovative Algorithms and Analysis, 141–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49262-9_5.

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González de Alaiza Martínez, Pedro, and María Elena Vázquez-Cendón. "Operator-Splitting on Hyperbolic Balance Laws." In Advances in Differential Equations and Applications, 279–87. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_27.

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Liotta, Salvatore Fabio, Vittorio Romano, and Giovanni Russo. "Central Schemes for Systems of Balance Laws." In Hyperbolic Problems: Theory, Numerics, Applications, 651–60. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8724-3_16.

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Conference papers on the topic "Hyperbolic balance laws"

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Kitsos, Constantinos, Gildas Besancon, and Christophe Prieur. "High-Gain Observer Design for a Class of Hyperbolic Systems of Balance Laws." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619291.

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Aloev, Rakhmatillo, and Dilfuza Nematova. "Lyapunov numerical stability of a hyperbolic system of linear balance laws with inhomogeneous coefficients." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0056862.

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Bartecki, Krzysztof. "Computation of transfer function matrices for 2×2 strongly coupled hyperbolic systems of balance laws." In 2013 Conference on Control and Fault-Tolerant Systems (SysTol). IEEE, 2013. http://dx.doi.org/10.1109/systol.2013.6693813.

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Bastin, Georges, Jean-Michel Coron, and Brigitte d'Andrea-Novel. "Boundary feedback control and Lyapunov stability analysis for physical networks of 2×2 hyperbolic balance laws." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4738857.

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Nourgaliev, Robert, Nam Dinh, and Theo Theofanous. "A Characteristics-Based Approach to the Numerical Solution of the Two-Fluid Model." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45551.

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This paper is concerned with numerical solutions of the two-fluid models of two-phase flow. The two-fluid modeling approach is based on the effective-field description of inter-penetrating continua and uses constitutive laws to account for the inter-field interactions. The effective-field balance equations are derived by a homogenization procedure and known to be non-hyperbolic. Despite their importance and widespread application, predictions by such models have been hampered by numerical pitfalls manifested in the formidable challenge to obtain convergent numerical solutions under computational grid refinement. At the root of the problem is the absence of hyperbolicity in the field equations and the resulting ill-posedness. The aim of the present work is to develop a high-order-accurate numerical scheme that is not subject to such limitations. The main idea is to separate conservative and non-conservative parts, by implementing the latter as part of the source term. The conservative part, being effectively hyperbolic, is treated by a characteristics-based method. The scheme performance is examined on a compressible-incompressible two-fluid model. Convergence of numerical solutions to the analytical one is demonstrated on a benchmark (water faucet) problem.

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Bertaglia, Giulia. "Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.13450.

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Mathematical models and numerical methods are a powerful resource for better understanding phenomena and processes throughout the fluid dynamics field, allowing significant reductions in the costs, which would otherwise be required to perform laboratory experiments, and even allowing to obtain useful data that could not be gathered through measurements.The correct characterization of the interactions that occur between the fluid and the wall that surrounds it is a fundamental aspect in all contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational method and the interpretation of the results and their application to cases of practical interest.In this work, innovative mathematical models able to predict the behavior of the fluid-structure interaction (FSI) mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented FSI systems in which the constitutive equation of the material is directly embedded into the system as partial differential equation [1]. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems [2]. To avoid the loss of accuracy in the stiff regimes of the proposed systems, asymptotic-preserving IMEX Runge-Kutta schemes are considered for the time discretization, which are able to maintain the consistency and the accuracy in the diffusive limit, without restrictions due to the scaling parameters [3]. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to in-vivo measurements for the latter.REFERENCES[1] Bertaglia, G., Caleffi, V. and Valiani, A. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system. Comput. Methods Appl. Mech. Eng., 360(C):112772 (2020).[2] Bertaglia, G., Ioriatti, M., Valiani, A., Dumbser, M. and Caleffi, V. Numerical methods for hydraulic transients in visco-elastic pipes. J. Fluids Struct., 81:230-254 (2018).[3] Pareschi, L. and Russo, G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput., 25:129-155 (2005).

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