Uniqueness of determination of a source function in a quasilinear inverse Stefan problem with final observation
type: Item
instance of: scholarly article
title: Uniqueness of determination of a source function in a quasilinear inverse Stefan problem with final observation
zbMATH Open document ID: 1257.80003
DOI: 10.1134/S1064562412030337
author: N. L. Gol'dman
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The author considers the inverse Stefan problem for the case where thermal coefficients are functions of time, position and temperature. The model consists of a one dimensional body of given length subject to change of phase. The problem is to find the temperature field in the given domain, the phase transition depending on time and the source function of initial functions, which are assumed to be given in direct Stefan problems. Also, the goal is to derive sufficient conditions ensuring the uniqueness of determining an unknown source in a quasi-linear inverse Stefan problem with additional information in the form of overdetermination. For such a problem, the author found the conditions imposed on the input data of the inverse Stefan problem, the uniqueness of a solution, and a class of admissible solutions of the inverse Stefan problem.
reviewed by: B. D. Vujanović
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 80A23
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6106474
MaRDI profile type: Publication
cites work: A method of fundamental solutions for the one-dimensional inverse Stefan problem
cites work: Properties of solutions of parabolic equations with unknown coefficients
cites work: Unique continuation for parabolic differential equations and inequalities
cites work: Q5520962
full work available at URL: s1064562412030337
OpenAlex ID: W2008788336
description: scientific article; zbMATH DE number 6106474