Analytical solution of Stefan-type problems

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2024-01-01 DOI:10.1515/jiip-2021-0077

Samat A. Kassabek, Targyn A. Nauryz, Amankeldy Toleukhanov

引用次数: 0

Abstract

In this paper, free surface problems of Stefan type for the parabolic heat equation are considered. The analytical solutions of the problems are based on the method of heat polynomials and integral error function in the form of series. Convergence of the series solution is considered and proved. Both one-and two-phase Stefan-type problems are investigated. Numerical results for one-phase inverse Stefan problem are presented and discussed.

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斯蒂芬型问题的解析解

本文考虑了抛物线热方程的斯特凡型自由表面问题。问题的解析解基于热多项式方法和数列形式的积分误差函数。考虑并证明了序列解的收敛性。研究了单相和两相斯特凡型问题。介绍并讨论了单相逆斯特凡问题的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography