Relevant bibliographies by topics / Hyperbolic balance law

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Hyperbolic balance law'

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Published: 9 March 2023

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Journal articles on the topic "Hyperbolic balance law"

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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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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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Barlow, Douglas A., Emilie LaVoie-Ingram, and Jahan Bayat. "Population-balance study of protein crystal growth from solution using a hyperbolic rate law." Journal of Crystal Growth 578 (January 2022): 126417. http://dx.doi.org/10.1016/j.jcrysgro.2021.126417.

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HBID, MY LHASSAN, EVA SÁNCHEZ, and RAFAEL BRAVO DE LA PARRA. "STATE-DEPENDENT DELAYS ASSOCIATED TO THRESHOLD PHENOMENA IN STRUCTURED POPULATION DYNAMICS." Mathematical Models and Methods in Applied Sciences 17, no. 06 (June 2007): 877–900. http://dx.doi.org/10.1142/s0218202507002145.

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The aim of this paper is to put in evidence the onset of state-dependent delays in threshold models for structured population dynamics. A unified approach to these models is provided, based on solving the corresponding balance law (hyperbolic P.D.E.) along the characteristic lines and showing the common underlying ideas. Size and age-structured models in different fields are presented: insect populations, cell proliferation and epidemics.
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Durur, Hülya. "Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method." Modern Physics Letters B 34, no. 03 (December 18, 2019): 2050036. http://dx.doi.org/10.1142/s0217984920500360.

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In this paper, an alternative method has been studied for traveling wave solutions of mathematical models which have an important place in applied sciences and balance term is not integer. With this method, the trigonometric, hyperbolic, complex and rational type traveling wave solutions of the (1[Formula: see text]+[Formula: see text]1)-dimensional resonant nonlinear Schrödinger’s (RNLS) equation with the parabolic law have constructed. This method can be applied reliably and effectively in many differential equations.
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Boyaval, Sébastien, and Mark Dostalík. "Non-isothermal viscoelastic flows with conservation laws and relaxation." Journal of Hyperbolic Differential Equations 19, no. 02 (June 2022): 337–64. http://dx.doi.org/10.1142/s0219891622500096.

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We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric energy density (function of the determinant of the deformation gradient det F and the temperature [Formula: see text] like the standard perfect-gas law or Noble–Abel stiffened-gas law) plus a polyconvex strain energy density function of F, [Formula: see text] and of symmetric positive-definite structure tensors that relax at a characteristic time scale. One feature of our model is that it unifies various ideal materials ranging from hyperelastic solids to perfect fluids, encompassing fluids with memory like Maxwell fluids. We establish a strictly convex mathematical entropy to show that the system is symmetric-hyperbolic. Another feature of the proposed model is therefore the short-time existence and uniqueness of smooth solutions, which define genuinely causal viscoelastic flows with waves propagating at finite speed. In heat-conductors, we complement the system by a Maxwell–Cattaneo equation for an energy-flux variable. The system is still symmetric-hyperbolic, and smooth evolutions with finite-speed waves remain well-defined.
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Said, Hamid. "An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy." Theoretical and Applied Mechanics, no. 00 (2020): 11. http://dx.doi.org/10.2298/tam200315011s.

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A simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian-Hamiltonian theory, integrals of motion, bracket formalism, and Noether?s theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.
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Meyer, Fabian, Christian Rohde, and Jan Giesselmann. "A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method." IMA Journal of Numerical Analysis 40, no. 2 (February 15, 2019): 1094–121. http://dx.doi.org/10.1093/imanum/drz004.

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Abstract In this article we present an a posteriori error estimator for the spatial–stochastic error of a Galerkin-type discretization of an initial value problem for a random hyperbolic conservation law. For the stochastic discretization we use the stochastic Galerkin method and for the spatial–temporal discretization of the stochastic Galerkin system a Runge–Kutta discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos (2016, Hyperbolic Conservation Laws in Continuum Physics, 4th edn., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 325, Berlin, Springer, pp. xxxviii+826), this leads to computable error bounds for the space–stochastic discretization error. Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretization. We conclude with some numerical examples confirming the theoretical findings.
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Wang, Yanli, and Shudao Zhang. "Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method." Communications in Computational Physics 21, no. 3 (February 7, 2017): 782–807. http://dx.doi.org/10.4208/cicp.220415.080816a.

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AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.
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Cai, Yifan, Quanyi Wang, Meng Liu, Yunqing Jiang, Tongfei Zou, Yunru Wang, Qingsong Li, et al. "Tensile Behavior, Constitutive Model, and Deformation Mechanisms of MarBN Steel at Various Temperatures and Strain Rates." Materials 15, no. 24 (December 7, 2022): 8745. http://dx.doi.org/10.3390/ma15248745.

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To reduce harmful gas emission and improve the operational efficiency, advanced ultra-supercritical power plants put forward higher requirements on the high temperature mechanical properties of applied materials. In this paper, the tensile behavior and deformation mechanisms of MarBN steel are discussed at different strain rates (5 × 10−3 s−1, 5 × 10−4 s−1, and 5 × 10−5 s−1) under room temperature and 630 °C. The results show that the tensile behavior of the alloy is dependent on temperature and strain rate, which derived from the balance between the average dislocation velocity and dislocation density. Furthermore, observed dynamic recrystallized grains under severe deformation reveal the existence of dynamic recovery at 630 °C, which increases the elongation compared to room temperature. Finally, three typical constitutive equations are used to quantitatively describe the tensile deformation behavior of MarBN steel under different strain rates and temperatures. Meanwhile, the constitutive model of flow stress for MarBN steel is developed based on the hyperbolic sine law.
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Dissertations / Theses on the topic "Hyperbolic balance law"

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Dalal, Abdulsalam Elmabruk Daw. "Shadow Wave Solutions for Some Balance Law Systems." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2017. https://www.cris.uns.ac.rs/record.jsf?recordId=104976&source=NDLTD&language=en.

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In the first part, the pressureless gas dynamic system with source (body force) is examined and solved by using Shadow Waves. The source represents gravity and Shadow Wave solution (containing the delta function) shows acceleration (contrary to shocks, for example). In the second part, one will nd numerical calculations that conrms the above results.
Rad je posvecen analizi modela gasa bez pritiska uz dodatak izvora. Model je resen koriscenjem senka talasa. U ovom slucaju, izvor predstavlja uticaj gravitacije na cestice u modelu. Za razliku od udarnih talasa, talasi senke koje sadrze delta funkciju, krecu se ubrzano pod gravitacionim uticajem. U drugom delu rada su naprevljeni numericki eksperimenti koji potvrdjuju teoijske rezultate.
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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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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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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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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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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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Books on the topic "Hyperbolic balance law"

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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 law"

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Ruggeri, Tommaso. "Universal Principles for Balance Law Systems." In Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 495–503. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-87871-7_60.

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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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Conference papers on the topic "Hyperbolic balance law"

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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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