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We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…

Numerical Analysis · Mathematics 2021-05-03 Sara Grundel , Michael Herty

In this paper, we introduce a hyperbolic model for entropy dissipative system of viscous conservation laws via a flux relaxation approach. We develop numerical schemes for the resulting hyperbolic relaxation system by employing the…

Numerical Analysis · Mathematics 2023-12-20 Tuowei Chen , Jiequan Li

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

Analysis of PDEs · Mathematics 2019-02-07 Swann Marx , Yacine Chitour , Christophe Prieur

We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…

Analysis of PDEs · Mathematics 2011-09-20 Christophe Berthon , Philippe G. LeFloch , Rodolphe Turpault

We study how isotropic and homogeneous far-from-equilibrium quantum systems relax to nonthermal attractors, which are of interest for cold atoms and nuclear collisions. We demonstrate that a first-order ordinary differential equation…

High Energy Physics - Theory · Physics 2024-02-19 Michal P. Heller , Aleksas Mazeliauskas , Thimo Preis

If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…

Soft Condensed Matter · Physics 2015-12-29 M. Popov , V. L. Popov , R. Pohrt

Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of small-amplitude shock profiles of general systems of coupled…

Analysis of PDEs · Mathematics 2015-05-13 Toan Nguyen , Ramon Plaza , Kevin Zumbrun

In a Lipschitz cylinder, this paper is devoted to establish an almost sharp error estimate $O(\varepsilon\log_2(1/\varepsilon))$ in $L^2$-norm for parabolic systems of elasticity with initial-Dirichlet conditions, arising in the…

Analysis of PDEs · Mathematics 2017-05-11 Qiang Xu , Shulin Zhou

We study nonlinear time-asymptotic stability of small--amplitude planar Lax shocks in a model consisting of a system of multi--dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics…

Analysis of PDEs · Mathematics 2011-08-18 Toan Nguyen

We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…

Analysis of PDEs · Mathematics 2012-10-18 Sebastiano Boscarino , Philippe G. LeFloch , Giovanni Russo

We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds,…

Probability · Mathematics 2025-08-01 Benjamin Fehrman , Benjamin Gess , Daniel Heydecker

We show the convergence of the zero relaxation limit in systems of $2 \times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation…

Analysis of PDEs · Mathematics 2018-11-01 James M. Scott , M. Paul Laiu , Cory D. Hauck

Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock…

Analysis of PDEs · Mathematics 2007-05-23 Olivier Gues , Guy Métivier , Mark Williams , Kevin Zumbrun

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…

Mathematical Physics · Physics 2009-04-14 Ahmad El Hajj , Régis Monneau

Aim of this paper is to extend the continuous dependence estimates proved in \cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic equations. As by-product of these estimates, we get an H\"older estimate for bounded…

Analysis of PDEs · Mathematics 2012-02-28 Fabio Camilli , Claudio Marchi

We establish nonlinear $H^2\cap L^1 \to H^2$ stability with sharp rates of decay in $L^p$, $p\geq 2$, of general hydraulic shock profiles, with or without subshocks, of the inviscid Saint-Venant equations of shallow water flow, under the…

Analysis of PDEs · Mathematics 2019-09-04 Zhao Yang , Kevin Zumbrun

We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously…

Analysis of PDEs · Mathematics 2024-11-26 Qian Huang , Christian Rohde , Wen-An Yong , Ruixi Zhang

In this paper on hyperbolic systems of conservation laws in one space dimension, we give a complete picture of stability for all solutions to the Riemann problem which contain only extremal shocks. We study stability of the Riemann problem…

Analysis of PDEs · Mathematics 2021-03-02 Sam G. Krupa

The hyperspherical adiabatic expansion method is used to describe correlations in a symmetric boson system rigorously confined to two spatial dimensions. The hyperangular eigenvalue equation turns out to be almost independent of the…

Soft Condensed Matter · Physics 2009-11-10 Han Guangze , O. Sørensen , A. S. Jensen , D. V. Fedorov

In this paper, we are concerned with the non-relativistic limit of a class of computable approximation models for radiation hydrodynamics. The models consist of the compressible Euler equations coupled with moment closure approximations to…

Analysis of PDEs · Mathematics 2022-04-18 Zhiting Ma , Wen-An Yong