Aggarwal, Aekta Vaidya, Ganesh Gowda, G. D. Veerappa
Published in
Zeitschrift für angewandte Mathematik und Physik

In this article, numerical schemes are proposed for approximating the solutions, possibly measure-valued with concentration (delta shocks), for a class of nonstrictly hyperbolic systems. These systems are known to model physical phenomena such as the collision of clouds and dynamics of sticky particles, for example. The scheme is constructed by ext...

Lai, Geng
Published in
Journal of Mathematical Fluid Mechanics

We study the existence of global continuous sonic–supersonic flows in a two-dimensional semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is sonic at the inlet of the duct. One of the main difficulties for the global existence is that the 2D steady Euler system becomes degenerate...

Sarrico, C.O.R.
Published in
Journal of Nonlinear Science

In the setting of a product of distributions, we define a concept of a solution for the Brio system ut+12(u2+v2)x=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{t}...

Wang, Qin Song, Kyungwoo
Published in
Acta Mathematica Scientia

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establi...

Dalibard, Anne-Laure Perrin, Charlotte

These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested profiles associated to the soft congestion Navier-Stokes system, we present a first local well-posedness result f...

Wang, Li
Published in
Acta Mathematica Scientia

The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations. In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection (vNR) and the other c...

Minhajul, Raja Sekhar, T.
Published in
Acta Mathematica Scientia

In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furtherm...

Dias, João-Paulo
Published in
Chinese Annals of Mathematics, Series B

In this paper, the author studies the local existence of strong solutions and their possible blow-up in time for a quasilinear system describing the interaction of a short wave induced by an electron field with a long wave representing an extension of the motion of the director field in a nematic liquid crystal’s asymptotic model introduced in [Sax...

Jenssen, Helge Kristian Luo, Yushuang
Published in
Zeitschrift für angewandte Mathematik und Physik

We consider self-similar solutions to the 1-dimensional isothermal Euler system for compressible gas dynamics. For eachβ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...

Ding, Min
Published in
Zeitschrift für angewandte Mathematik und Physik

This article is devoted to studying one-dimensional piston problem for the compressible Magnetohydrodynamics when the piston is pushed forward relatively. If the initial data and the piston speed are both given some small BV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage...