Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation
zbMATH Open document ID: 0654.76116
DOI: 10.1016/0167-2789(87)90006-6
published in: Physica D
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://dspace.library.uu.nl/handle/1874/17168
review text: A nonlinear diffusion equation is considered which models the temperature distribution in a laser-sustained plasma subject to wind. As certain parameters are small a singular perturbation problem arises and the method of matched asymptotic expansions is applied to approximate the solution. An essential role in this problem is played by the plasma front. This is a free surface separating the plasma and non-plasma phases. One of the main results is that we derive a 1st order nonlinear P.D.E. of Hamilton-Jacobi type, which describes certain parts of the free surface in the stationary case. This equation is analyzed for various wind directions. It appears that for the initial conditions for these parts of this free surface there are different possibilities depending on the wind direction. We show further that the solution of the Hamilton-Jacobi equation can contain singularities of corner type. Furthermore, the effect of wind on the stability region of the stationary full plasma solution is analyzed. The method of analysis presented in this paper is not restricted to the cone-like geometry or the specific form of the non-linearity of the problem considered here, but has potentially a much wider scope. However, the case under study in this paper is certainly representative for the effects that have to be taken into account.
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 70H25
zbMATH DE Number: 4068544
zbMATH Keywords: nonlinear diffusion equation
zbMATH Keywords: temperature distribution
zbMATH Keywords: laser-sustained plasma
zbMATH Keywords: singular perturbation problem
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: Hamilton- Jacobi equation
author: Wiktor Eckhaus
author: Aart van Harten
author: Zbigniew Peradzyński
MaRDI profile type: Publication
OpenAlex ID: W2125677939
cites work: A Singularly Perturbed Free Boundary Problem Describing a Laser Sustained Plasma
cites work: Q3853988
cites work: Q3999241
description: scientific article; zbMATH DE number 4068544