Ebook: Mathematical Modelling of Heat and Mass Transfer Processes
- Tags: Partial Differential Equations, Approximations and Expansions, Applications of Mathematics, Math. Applications in Chemistry, Fluid- and Aerodynamics
- Series: Mathematics and Its Applications 348
- Year: 1995
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
In the present book the reader will find a review of methods for constructing a certain class of asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons, kinks, traveling waves, etc. It can be said that either the solutions from this class or their derivatives are localized in the neighborhood of a certain curve or surface. For the present edition, the book published in Moscow by the Nauka publishing house in 1987, was almost completely revised, essentially up-dated, and shows our present understanding of the problems considered. The new results, obtained by the authors after the Russian edition was published, are referred to in footnotes. As before, the book can be divided into two parts: the methods for constructing asymptotic solutions ( Chapters I-V) and the application of these methods to some concrete problems (Chapters VI-VII). In Appendix a method for justification some asymptotic solutions is discussed briefly. The final formulas for the asymptotic solutions are given in the form of theorems. These theorems are unusual in form, since they present the results of calculations. The authors hope that the book will be useful to specialists both in differential equations and in the mathematical modeling of physical and chemical processes. The authors express their gratitude to Professor M. Hazewinkel for his attention to this work and his support.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-18
Properties of Exact Solutions of Nondegenerate and Degenerate Ordinary Differential Equations....Pages 19-34
Direct Methods for Constructing Exact Solutions of Semilinear Parabolic Equations....Pages 35-73
Singularities of Nonsmooth Solutions to Quasilinear Parabolic and Hyperbolic Equations....Pages 74-126
Wave Asymptotic Solutions of Degenerate Semilinear Parabolic and Hyperbolic Equations....Pages 127-200
Finite Asymptotic Solutions of Degenerate Equations....Pages 201-234
Models for Mass Transfer Processes....Pages 235-253
The Flow Around a Flat Plate....Pages 254-294
Back Matter....Pages 295-323
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-18
Properties of Exact Solutions of Nondegenerate and Degenerate Ordinary Differential Equations....Pages 19-34
Direct Methods for Constructing Exact Solutions of Semilinear Parabolic Equations....Pages 35-73
Singularities of Nonsmooth Solutions to Quasilinear Parabolic and Hyperbolic Equations....Pages 74-126
Wave Asymptotic Solutions of Degenerate Semilinear Parabolic and Hyperbolic Equations....Pages 127-200
Finite Asymptotic Solutions of Degenerate Equations....Pages 201-234
Models for Mass Transfer Processes....Pages 235-253
The Flow Around a Flat Plate....Pages 254-294
Back Matter....Pages 295-323
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