Inverse Stefan Problems - Couverture souple

Gol'dman, N.L.

Couverture souple

ISBN 10 : 9401063095 ISBN 13 : 9789401063098

Editeur : Springer, 2012

Synopsis

In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed. The study of this new class of ill-posed problems is motivated by the needs of the mod- eling and control of nonlinear processes with phase transitions in thermophysics and mechanics of continuous media. Inverse Stefan problems are important for the perfection of technologies both in high temperature processes (e.g., metallurgy, the aircraft industry, astronautics and power engineering) and in hydrology, exploitation of oil-gas fields, etc. The proposed book will complete a gap in these subjects in the preceding re- searches of ill-posed problems. It contains the new theoretical and applied studies of a wide class of inverse Stefan problems. The statements of such problems on the determination of boundary functions and coefficients of the equation are considered for different types of additional information about their solution. The variational method of obtaining stable approximate solutions is proposed and established. It is implemented by an efficient computational scheme of descriptive regularization. This algorithm utilizes a priori knowledge of the qualitative structure of the sought solution and ensures a substantial saving in computational costs. It is tested on model and applied problems in nonlinear thermophysics. In particular, the results of calculations for important applications in continuous casting of ingots and in the melting of a plate with the help of laser technology are presented.

A propos du livre

Présentation de l'éditeur

This monograph presents a new theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in domains with free boundaries. This new approach to the theory of ill-posed problems is useful for the modelling of nonlinear processes with phase transforms in thermophysics and mechanics of continuous media.
Regularisation methods and algorithms are developed for the numerical solution of inverse Stefan problems ensuring substantial savings in computational costs. Results of calculations for important applications in a continuous casting and for the treatment of materials using laser technology are also given.
Audience: This book will be of interest to post-graduate students and researchers whose work involves partial differential equations, numerical analysis, phase transformation, mathematical modelling, industrial mathematics and the mathematics of physics.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 9401063095
• ISBN 13: 9789401063098
• Reliure: Broché
• Nombre de pages: 268
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne