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Inverse Stefan Problems

Author: N L Gol'dman
Publisher: Dordrecht : Springer Netherlands, 1997.
Series: Mathematics and Its Applications, 412.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: N L Gol'dman
ISBN: 9789401154888 9401154880
OCLC Number: 851380529
Description: 1 online resource (viii, 250 pages).
Contents: Basic Designations --
1 Statements of Quasilinear Inverse Stefan Problems --
1.1 Classification of ill-posed inverse Stefan problems and their applications --
1.2 One-phase boundary inverse Stefan problems with given phase boundaries --
1.3 One-phase boundary inverse Stefan problems with unknown phase boundaries --
1.4 Boundary inverse Stefan problems in the two-phase case --
1.5 Coefficient inverse Stefan problems --
2 The Regularization Variational Method for Solving Inverse Stefan Problems --
2.1 Construction of approximate solutions on the basis of the quasi-solution method --
2.2 Stability of approximate solutions --
2.3 Differentiability of functionals in the variational formulations of inverse Stefan problems --
3 Algorithms for the Numerical Solution of Inverse Stefan Problems --
3.1 Principles of construction of algorithms --
3.2 Numerical solution of the one-phase inverse Stefan problems with given phase boundaries. Determination of boundary regimes for continuous casting --
3.3 Descriptive regularization algorithms for boundary inverse Stefan problems with unknown phase boundaries --
3.4 Numerical solution of coefficient inverse Stefan problems. Determination of the intensity of laser sources --
4 Properties of Operator Representations of Inverse Stefan Problems --
4.1 On classical solvability of quasilinear moving boundary problems --
4.2 A priori estimates of Hölder norms for the differential-difference analogs of linear parabolic equations --
4.3 Unique solvability in the Hölder spaces of the differential-difference analogs of the quasilinear boundary-value problems --
4.4 Global existence, uniqueness and stability in the Hölder spaces for the direct quasilinear Stefan problems.
Series Title: Mathematics and Its Applications, 412.
Responsibility: by N.L. Gol'dman.

Abstract:

In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed.  Read more...

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