American Mathematical Society
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Introduction. Traveling Waves Described by Parabolic Systems
1. Classification of waves
2. Existence of waves
3. Stability of waves
4. Wave propagation speed
5. Bifurcations of waves
6. Traveling waves in physics, chemistry, and biology
Part I. Stationary Waves
Chapt 1. Scalar Equation
1. Introduction
2. Functionals and
3. Waves and systems of waves
4. Properties of solutions of parabolic equations
5. Approach to waves and systems of waves
6. Supplement (Additions and bibliographic commentaries)
Chapt 2. Leray-Schauder Degree
1. Introduction. Formulation of results
2. Estimate of linear operators from below
3. Functional c(u) and operator A(u)
4. Leray-Schauder degree
5. Linearized operator
6. Index of a stationary point
7. Supplement. Leray-Schauder degree in the multidimensional case
Chapt 3. Existence of Waves
1. Introduction. Formulation of results
2. A priori estimates
3. Existence of monotone waves
4. Monotone systems
5. Supplement and bibliographic commentaries
Chapt 4. Structure of the Spectrum
1. Elliptic problems with a parameter
2. Continuous spectrum
3. Structure of the spectrum
4. Examples
5. Spectrum of monotone systems
Chapt 5. Stability and Approach to a Wave
1. Stability with shift and its connection with the spectrum
2. Stability of planar waves to spatial perturbations
3. Conditions of instability
4. Stability of waves for monotone systems
5. On the solutions of nonstationary problems
6. Approach to a monotone wave
7. Minimax representation of the speed
Part II. Bifurcation of Waves
Chapt 6. Bifurcation of Nonstationary Modes of Wave Propagation
1. Statement of the problem
2. Representation of solutions in series form. Stability of solutions
3. Examples
Chapt 7. Mathematical Proofs
1. Statement of the problem and linear analysis
2. General representation of solutions of the nonlinear problem. Existence of solutions
3. Stability of branching-off solutions
Part III. Waves in Chemical Kinetics and Combustion
Chapt 8. Waves in Chemical Kinetics
1. Equations of chemical kinetics
2. Monotone systems
3. Existence and stability of waves
4. Branching chain reactions
5. Other model systems
Bibliographic commentaries
Chapt 9. Combustion Waves with Complex Kinetics
1. Introduction
2. Existence of waves for kinetic systems with irreversible reactions
3. Stability of a wave in the case of equality of transport coefficients
4. Examples
Chapt 10. Estimates and Asymptotics of the Speed of Combustion Waves
1. Estimates for the speed of a combustion wave in a condensed medium
2. Estimates for the speed of a gas combustion wave
3. Determination of asymptotics of the speed by the method of successive approximations
Supplement. Asymptotic and Approximate Analytical Methods in Combustion Problems
1. Narrow reaction zone method. Speed of a stationary combustion wave
2. Stability of a stationary combustion wave
3. Nonadiabatic combustion
4. Stage combustion
5. Transformations in a combustion wave
6. Application of the methods of bifurcation theory to the study of nonstationary modes of propagation of combustion waves
7. Surveys and monographs
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