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Mathematical modelling of heat and mass transfer processes. Evolution of dissipative structures. (Matematicheskoe modelirovanie protsessov teplomassoperenosa. Ehvolyutsiya dissipativnykh struktur). (Russian) Zbl 0645.73049

Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 352 p., R. 5.40 (1987).
This textbook gives a systematic and extensive exposition of some of the main questions regarding the mathematical modelling of mass-transfer processes. The mathematical models of mass-transfer in chemical reactions appearing in microelectronics technology, of the heterogeneous processes, of the thermal oxidation of silicon, etc. are constructed. The evolution of the considered models are described by systems of quasi-linear parabolic and hyperbolic equations. The authors are studying the structure of singularities of nonsmooth solutions of quasi-linear parabolic and hyperbolic systems with small parameters, the asymptotic solutions, and their behaviour as the small parametes approach zero, etc. A new method is given to obtain the asymptotic localization of the solutions of systems governing the evoluton of the considered models.
The book provides an accurate picture of current research in the field, is well written, and contains an up-to-date reference literature. The book is addressed to a wide group of physicists, scientific chemists, engineers, and mathematicians.
Reviewer: Gh.Gr.Ciobanu

MSC:

74A15 Thermodynamics in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
35B65 Smoothness and regularity of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
80A32 Chemically reacting flows