Mathematical Modelling of Heat and Mass Transfer Processes: Mathematics and Its Applications, cartea 348
Autor V.G. Danilov, Victor P. Maslov, K. a. Volosoven Limba Engleză Paperback – 23 oct 2012
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Specificații
ISBN-13: 9789401041836
ISBN-10: 9401041830
Pagini: 336
Ilustrații: IX, 323 p.
Dimensiuni: 160 x 240 x 18 mm
Greutate: 0.47 kg
Ediția:Softcover reprint of the original 1st ed. 1995
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9401041830
Pagini: 336
Ilustrații: IX, 323 p.
Dimensiuni: 160 x 240 x 18 mm
Greutate: 0.47 kg
Ediția:Softcover reprint of the original 1st ed. 1995
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchCuprins
I. Properties of Exact Solutions of Nondegenerate and Degenerate Ordinary Differential Equations.- 1.1. Standard equations.- 1.2. Examples.- II. Direct Methods for Constructing Exact Solutions of Semilinear Parabolic Equations.- 2.1. Preliminary notes.- 2.2. Representation of self-similar solutions in terms of rational functions.- 2.3. Construction of exact one-phase and two-phase solutions.- 2.4. Formulas for solutions of semilinear parabolic equations with common cubic nonlinearity.- 2.5. Relation between the number of phases in the solution and the degree of nonlinearity.- 2.6. Asymptotics of wave creation for the KPP-Fisher equation.- III. Singularities of Nonsmooth Solutions to Quasilinear Parabolic and Hyperbolic Equations.- 3.1. Main definitions.- 3.2. Asymptotic solutions bounded as ? ? 0.- 3.3. Asymptotic solutions unbounded as ? ? 0.- 3.4. The structure of singularities of solutions to quasilinear parabolic equations near the boundary of the solution support.- 3.5. The structure of singularities of nonsmooth self-similar solutions to quasilinear hyperbolic equations.- IV. Wave Asymptotic Solutions of Degenerate Semilinear Parabolic and Hyperbolic Equations.- 4.1. Self-stabilizing asymptotic solutions.- 4.2. Construction of nonsmooth asymptotic solutions. Derivation of basic equations.- 4.3. Global localized solutions and regularization of ill-posed problems.- 4.4. Asymptotic behavior of localized solutions to equations with variable coefficients.- 4.5. Heat wave propagation in nonlinear media. Asymptotic solutions to hyperbolic heat (diffusion) equation.- 4.6. Localized solutions in the multidimensional case.- V. Finite Asymptotic Solutions of Degenerate Equations.- 5.1. An example of constructing an asymptotic solution.- 5.2. Asymptotic solutions in theone-dimensional case.- 5.3. Asymptotic finite solutions of degenerate quasilinear parabolic equations with small diffusion.- 5.4. Relation between approximate solutions of quasilinear parabolic and parabolic equations.- VI. Models for Mass Transfer Processes.- 6.1. Nonstationary models of mass transfer.- 6.2. Asymptotic solution to the kinetics equation of nonequilibrium molecular processes with external diffusion effects.- 6.3. The simplest one-dimensional model.- VII. The Flow around a Plate.- 7.1. Introduction.- 7.2. Uniformly suitable asymptotic solution to the problem about the flow of low-viscous liquid around a semi-infinite thin plate.- 7.3. Asymptotic behavior of the laminar flow around a plate with small periodic irregularities.- 7.4. Critical amplitude and vortices in the flow around a plate with small periodic irregularities.- References.- Appendix. Justification of Asymptotic Solutions.- 1. One-dimensional scalar case.- 3. Zeldovich waves.