On a nonlinear moving boundary problem with heterogeneity: Application of a reciprocal transformation
type: Item
instance of: scholarly article
title: On a nonlinear moving boundary problem with heterogeneity: Application of a reciprocal transformation
zbMATH Open document ID: 0661.35087
DOI: 10.1007/BF00945727
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: In recent work it has been shown that a reciprocal transformation may be used to obtain a parametric representation of the solution to an important class of nonlinear moving boundary problems. Here, use is made of a result due to Broadbridge to incorporate a degree of heterogeneity into the class of nonlinear media for which the solution may be constructed. The nonlinear transport equation in the posed boundary value problem is of a type that arises as an evaporation model in soil mechanics. The exact solution obtained representes an extension of the classical Neumann solution.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 4080065
zbMATH Keywords: reciprocal transformation
zbMATH Keywords: parametric representation
zbMATH Keywords: moving boundary
zbMATH Keywords: nonlinear media
zbMATH Keywords: nonlinear transport equation
zbMATH Keywords: evaporation model
zbMATH Keywords: Neumann solution
author: Colin Rogers
author: Philip Broadbridge
MaRDI profile type: Publication
cites work: Application of a reciprocal transformation to a two-phase Stefan problem
cites work: On a class of moving boundary problems in non-linear heat conduction: application of a Bäcklund transformation
cites work: Q5785591
cites work: Heat Conduction in Simple Metals
cites work: On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)]−(∂u/∂t)=0
cites work: Bäcklund transformations and their applications
full work available at URL: https://doi.org/10.1007/bf00945727
OpenAlex ID: W2093572986
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description: scientific article; zbMATH DE number 4080065