Relevant bibliographies by topics / Diagonal hyperbolic systems

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  1. Journal articles
  2. Dissertations / Theses
  3. Conference papers

Academic literature on the topic 'Diagonal hyperbolic systems'

Author: Grafiati
Published: 17 August 2022
Last updated: 16 September 2022

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Journal articles on the topic "Diagonal hyperbolic systems"

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EL HAJJ, AHMAD, and RÉGIS MONNEAU. "GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA." Journal of Hyperbolic Differential Equations 07, no. 01 (March 2010): 139–64. http://dx.doi.org/10.1142/s0219891610002050.

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In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonal hyperbolic system appears naturally in the modeling of the dynamics of dislocation densities.
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EL HAJJ, AHMAD, and RÉGIS MONNEAU. "UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA." Journal of Hyperbolic Differential Equations 10, no. 03 (September 2013): 461–94. http://dx.doi.org/10.1142/s0219891613500161.

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We study the uniqueness of solutions to diagonal hyperbolic systems in one spatial dimension and we present two uniqueness results. First, we establish a global existence and uniqueness theorem for continuous solutions to strictly hyperbolic systems. Second, we establish a global existence and uniqueness theorem for Lipschitz continuous solutions to hyperbolic systems that need not be strictly hyperbolic. Furthermore, an application is presented for one-dimensional flows in isentropic gas dynamics.
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Colombini, Ferruccio, and Daniele Del Santo. "Blow-up for hyperbolic systems in diagonal form." Nonlinear Differential Equations and Applications 8, no. 4 (November 2001): 465–72. http://dx.doi.org/10.1007/pl00001458.

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Spehner, D. "Spectral form factor of hyperbolic systems: leading off-diagonal approximation." Journal of Physics A: Mathematical and General 36, no. 26 (June 17, 2003): 7269–90. http://dx.doi.org/10.1088/0305-4470/36/26/304.

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Jourdain, Benjamin, and Julien Reygner. "A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data." Journal of Hyperbolic Differential Equations 13, no. 03 (September 2016): 441–602. http://dx.doi.org/10.1142/s0219891616500144.

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This paper is devoted to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions or, more generally, nonconstant monotonic bounded functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic fields, we construct a multi-type version of the sticky particle dynamics and we obtain the existence of global weak solutions via a compactness argument. We then derive a [Formula: see text] stability estimate on the particle system which is uniform in the number of particles. This allows us to construct nonlinear semigroups solving the system in the sense of Bianchini and Bressan [Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math. (2) 161(1) (2005) 223–342]. We also obtain that these semigroup solutions satisfy a stability estimate in Wasserstein distances of all order, which extends the classical [Formula: see text] estimate and generalizes to diagonal systems a result by Bolley, Brenier and Loeper [Contractive metrics for scalar conservation laws, J. Hyperbolic Differ. Equ. 2(1) (2005) 91–107] in the scalar case. Our results are established without any smallness assumption on the variation of the data, and we only require the characteristic fields to be Lipschitz continuous and the system to be uniformly strictly hyperbolic.
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Li, Ta-Tsien, and Yue-Jun Peng. "Cauchy problem for weakly linearly degenerate hyperbolic systems in diagonal form." Nonlinear Analysis: Theory, Methods & Applications 55, no. 7-8 (December 2003): 937–49. http://dx.doi.org/10.1016/j.na.2003.08.010.

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Dus, Mathias, Francesco Ferrante, and Christophe Prieur. "On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 23. http://dx.doi.org/10.1051/cocv/2019069.

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This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.
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OHWA, HIROKI. "THE SHOCK CURVE APPROACH TO THE RIEMANN PROBLEM FOR 2 × 2 HYPERBOLIC SYSTEMS OF CONSERVATION LAWS." Journal of Hyperbolic Differential Equations 07, no. 02 (June 2010): 339–64. http://dx.doi.org/10.1142/s0219891610002128.

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We consider the Riemann problem for 2 × 2 hyperbolic systems of conservation laws in one space variable. Our main assumptions are that the product of non-diagonal elements within the Fréchet derivative (Jacobian) of the flux is positive, and that the system is genuinely nonlinear. The first assumption implies that the system is strictly hyperbolic, but we do not require a convexity-like condition such as the Smoller–Johnson condition. By using the shock curve approach, we show that those two assumptions are sufficient to establish the uniqueness of self-similar solutions satisfying the Lax entropy conditions at discontinuities.
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Li, Tatsien, and Zhiqiang Wang. "Global exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form." International Journal of Dynamical Systems and Differential Equations 1, no. 1 (2007): 12. http://dx.doi.org/10.1504/ijdsde.2007.013741.

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Yu, Lixin. "Global exact boundary observability for first-order quasilinear hyperbolic systems of diagonal form." Mathematical Methods in the Applied Sciences 35, no. 13 (June 22, 2012): 1505–17. http://dx.doi.org/10.1002/mma.2520.

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Dissertations / Theses on the topic "Diagonal hyperbolic systems"

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Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.

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Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en démontrant un résultat similaire pour un système d’équations de type eikonal non-linéaire qui est en fait une généralisation du système hyperbolique déjà étudié. En effet, nous prouvons aussi l’existence et l’unicité d’une solution continue pour le système eikonal. Ensuite, nous nous sommes intéressés à l’analyse numérique de ce système en proposant un schéma aux différences finies, par lequel nous montrons la convergence vers le problème continu et nous consolidons nos résultats avec quelques simulations numériques. Dans une autre direction, nous nous sommes intéressés à la théorie de contraction différentielle pour les équations d’évolutions. Après avoir introduit une nouvelle distance, nous construisons une nouvelle famille des solutions contractantes positives pour l’équation d’évolution p-Laplace
In this thesis, we are mainly interested in the theoretical and numerical study of certain equations that describe the dynamics of dislocation densities. Dislocations are microscopic defects in materials, which move under the effect of an external stress. As a first work, we prove a global in time existence result of a discontinuous solution to a diagonal hyperbolic system, which is not necessarily strictly hyperbolic, in one space dimension. Then in another work, we broaden our scope by proving a similar result to a non-linear eikonal system, which is in fact a generalization of the hyperbolic system studied first. We also prove the existence and uniqueness of a continuous solution to the eikonal system. After that, we study this system numerically in a third work through proposing a finite difference scheme approximating it, of which we prove the convergence to the continuous problem, strengthening our outcomes with some numerical simulations. On a different direction, we were enthused by the theory of differential contraction to evolutionary equations. By introducing a new distance, we create a new family of contracting positive solutions to the evolutionary p-Laplacian equation
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Conference papers on the topic "Diagonal hyperbolic systems"

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Thompson, Lonny L., and Prapot Kunthong. "Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15753.

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The time-discontinuous Galerkin (TDG) method possesses high-order accuracy and desirable C-and L-stability for second-order hyperbolic systems including structural acoustics. C- and L-stability provide asymptotic annihilation of high frequency response due to spurious resolution of small scales. These non-physical responses are due to limitations in spatial discretization level for large-complex systems. In order to retain the high-order accuracy of the parent TDG method for high temporal approximation orders within an efficient multi-pass iterative solution algorithm which maintains stability, generalized gradients of residuals of the equations of motion expressed in state-space form are added to the TDG variational formulation. The resultant algorithm is shown to belong to a family of Pade approximations for the exponential solution to the spatially discrete hyperbolic equation system. The final form of the algorithm uses only a few iteration passes to reach the order of accuracy of the parent solution. Analysis of the multi-pass algorithm shows that the first iteration pass belongs to the family of (p+1)-stage stiff accurate Singly-Diagonal-Implicit-Runge-Kutta (SDIRK) method. The methods developed can be viewed as a generalization to the SDIRK method, retaining the desirable features of efficiency and stability, now extended to high-order accuracy. An example of a transient solution to the scalar wave equation demonstrates the efficiency and accuracy of the multi-pass algorithms over standard second-order accurate single-step/single-solve (SS/SS) methods.
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Thompson, Lonny L., and Dantong He. "Adaptive Time-Discontinuous Galerkin Methods for Acoustic Scattering in Unbounded Domains." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32737.

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Comprehensive adaptive procedures with efficient solution algorithms for the time-discontinuous Galerkin space-time finite element method (DGFEM) including high-order accurate nonreflecting boundary conditions (NRBC) for unbounded wave problems are developed. Sparse multi-level iterative schemes are developed to solve the resulting system equations for the interior hyperbolic equations coupled with the first-order equations associated with auxiliary functions in the NRBC. The iterative strategy requires only a f ew iterations per time step to resolve the solution to high accuracy. Further cost savings are obtained by diagonalizing the mass and boundary damping matrices. In this case the algebraic structure decouples the diagonal block matrices giving rise to an unconditionally stable explicit iterative method. An h-adaptive space-time strategy is employed based on the superconvergent patch recovery (SPR) technique, together with a temporal error estimate arising from the discontinuous jump between time steps. For accurate data transfer (projection) between meshes, we develop a new superconvergent interpolation (SI) method. Numerical studies of transient scattering demonstrate the accuracy, reliability and efficiency gained from the adaptive strategy.
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