Parametric dependence of phase boundary solution to model kinetic equations
type: Item
instance of: scholarly article
title: Parametric dependence of phase boundary solution to model kinetic equations
zbMATH Open document ID: 1099.76502
author: Bogdan Kazmierczak
author: Piechór Kazimierz
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2003-03-27T00:00:00Z
review text: We study travelling wave solutions of a four-velocity model of van der Waals fluids, connecting two equilibrium states, which are saddle critical points of the corresponding dynamic system. Solutions of this type are interpreted as dynamic phase transitions. We look for solutions which are a perturbation of Maxwell line solution describing equilibrium phase changes. Using the implicit function theorem, we show that, under some additional assumptions, there exists a unique travelling wave to our model, and that it is continuously differentiable with respect to the parameters of the problem. Also, given the left state of rest, we obtain an approximate expression for the wave speed. From this formula we infer that the ``kinetic'' wave speed is different from the one obtained from the hydrodynamic approximation.
Mathematics Subject Classification ID: 76A99
Mathematics Subject Classification ID: 82B26
zbMATH DE Number: 1889131
zbMATH Keywords: four-velocity model
zbMATH Keywords: van der Waals fluids
zbMATH Keywords: dynamic phase transitions
MaRDI profile type: Publication
full work available at URL: s00033-002-8168-1
OpenAlex ID: W1551091263
DOI: 10.1007/S00033-002-8168-1
description: scientific article; zbMATH DE number 1889131