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Related papers: Relaxation limit for Aw-Rascle system

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We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated…

Analysis of PDEs · Mathematics 2018-02-20 Hung Luong , Norbert Mauser , Jean-Claude Saut

On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…

Soft Condensed Matter · Physics 2009-10-30 Gongwen Peng , Takao Ohta

A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…

Numerical Analysis · Mathematics 2021-12-23 Alan F. Hegarty , Eugene O'Riordan

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…

Analysis of PDEs · Mathematics 2021-10-12 Mohamed Ghattassi , Xiaokai Huo , Nader Masmoudi

This paper analyzes the vanishing pressure limit of solutions to the Aw-Rascle model and the perturbed Aw-Rascle model for modified Chaplygin gas. Firstly, the Riemann problem of the Aw-Rascle model is solved constructively. A special delta…

Analysis of PDEs · Mathematics 2014-10-07 Jinhuan Wang , Jinjing Liu , Hanchun Yang

The Navier-Stokes-Cahn-Hilliard (NSCH) system governs the diffuse-interface dynamics of two incompressible and immiscible fluids. We consider a relaxation approximation of the NSCH system that is composed by a system of first-order…

Numerical Analysis · Mathematics 2026-01-27 Jan Giesselmann , Jens Keim , Fabio Leotta , Christian Rohde

The fundamental Filippov-Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation…

Dynamical Systems · Mathematics 2007-05-23 Brian P. Ingalls , Eduardo D. Sontag , Yuan Wang

We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…

Numerical Analysis · Mathematics 2022-05-05 Wenbin Dong , Hansong Tang

In this paper we study weak-strong uniqueness and singular relaxation limits for the Euler--Korteweg and Navier--Stokes--Korteweg systems with non monotone pressure. Both weak-strong uniqueness and the relaxation limit are investigated…

Analysis of PDEs · Mathematics 2025-09-10 Giada Cianfarani Carnevale , Jan Giesselmann

In this article, we study the small dispersion limit of the Euler-Korteweg system in a domain with a smooth boundary and no-flux boundary conditions. We exploit a relative energy approach to study the convergence of finite energy weak…

Analysis of PDEs · Mathematics 2026-04-28 Paolo Antonelli , Yuri Cacchiò

In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice…

Numerical Analysis · Mathematics 2020-04-21 Sohrab Valizadeh , Alaeddin Malek , Abdollah Borhanifar

This paper discusses the dynamical properties of $p$-spin models with Kac kind interactions. For large but finite interaction range $R$ one finds two different time scales for relaxation. A first relaxation roughly independent of $R$ where…

Statistical Mechanics · Physics 2008-09-16 Silvio Franz

This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various…

Optimization and Control · Mathematics 2020-12-24 Arash Farokhi Soofi , Saeed D. Manshadi

We consider self-similar approximations of nonlinear hyperbolic systems in one space dimension with Riemann initial data and general diffusion matrix. We assume that the matrix of the system is strictly hyperbolic and the diffusion matrix…

Analysis of PDEs · Mathematics 2008-12-16 K. T. Joseph , Philippe G. LeFloch

We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test…

Analysis of PDEs · Mathematics 2017-01-06 Ludovic Cesbron , Harsha Hutridurga

An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and…

Materials Science · Physics 2009-10-30 Steven P. Lewis , M. V. Pykhtin , E. J. Mele , Andrew M. Rappe

This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a…

Disordered Systems and Neural Networks · Physics 2009-11-13 Alexander V. Milovanov , Jens Juul Rasmussen , Kristoffer Rypdal

In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-fluid models. First, we justify the pressure-relaxation limit from a…

Analysis of PDEs · Mathematics 2024-04-22 Timothée Crin-Barat , Ling-Yun Shou , Jin Tan

In this paper, we are concerned with a model of polytropic gas flow, which consists the mass equation, the momentum equation and a varying entropy equation. First, a new technique, to set up a relation between the Riemann invariants of the…

Analysis of PDEs · Mathematics 2020-04-17 Yun-guang Lu

Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…

Analysis of PDEs · Mathematics 2023-12-13 Rui Jin , Yachun Li , Liang Zhao