Patterns and Waves: Qualitative Analysis of Nonlinear Differential Equations

✍ Scribed by Takaaki Nishida; Masayasu Mimura; Hiroshi Fujii

• Publisher: North Holland
• Year: 1986
• Tongue: English
• Leaves: 709
• Category: Library

✦ Synopsis

Part I of this volume surveys the developments in the analysis of nonlinear phenomena in Japan during the past decade, while Part II consists of up-to-date original papers concerning qualitative theories and their applications. Dealt with here are nonlinear problems related to general analysis, fluid dynamics, mathematical biology and computer sciences, and their underlying mathematical structures, e.g. nonlinear waves and propagations, bifurcation phenomena, chaotic phenomena, and fractals. The volume is dedicated to Professor Masaya Yamaguti in celebration of his 60th birthday.

✦ Table of Contents

Patterns and Waves: Qualitative Analysis of Nonlinear Differential Equations
Copyright Page
Preface
The Soul of Mathematics
Contents
Part I
Section 1: Hyperbolic Partial Differential Equations
Chapter 1. On Weakly Hyperbolic Equations with Constant Multiplicities
Chapter 2. Strongly Hyperbolic Equations and their Applications
Section 2: Flow Problems
Chapter 3. Solutions of the Boltzmann Equation
Chapter 4. Equations of Motion of Compressible Viscous Fluids
Section 3: Reaction-Diffusion Equations
Chapter 5. Predation-Mediated Coexistence and Segregation Structures
Chapter 6. On the Structure of Multiple Existence of Stable Stationary Solutions in Systems of Reaction-Diffusion Equations
Section 4: Chaos and Fractals
Chapter 7. Chaotic Phenomena and Fractal Objects in Numerical Analysis
Chapter 8. Fractals in Mathematics
Section 5: Numerical Analysis & Computations
Chapter 9. Parallel Computation
Chapter 10. A Theoretical and Computational Study of Upwind-Type Finite Element Methods
Part II
Chapter 11. Positive Solutions to Some Semilinear Elliptic Equations in L1(RN)
Chapter 12. On the Vlasov-Poisson Limit of the Vlasov-Maxwell Equation
Chapter 13. A Discrete Model for Spatially Aggregating Phenomena
Chapter 14. A Note on the Blowing-up Problem of a Certain System of Nonlinear Parabolic Equations
Chapter 15. L Equation de Kadomtsev-Petviashvili approchant les ondes longues de surface de I'eau en 'ecoulement trois-dimensionnel
Chapter 16. Application of an Iteration Scheme to the Analysis of Incompressible or Nearly Incompressible Media
Chapter 17. On a Local Existence Theorem for the Evolution Equation of Gaseous Stars
Chapter 18. Fundamental Solution of the Linearized System for the Exterior Stationary Problem of Compressible Viscous Flow
Chapter 19. Nonlocal Advection Effect on Bistable Reaction-Diffusion Equations
Chapter 20. On Small Data Scattering for Some Nonlinear Wave Equations
Chapter 21. The Near-field Finite Difference Approximation for Wave Propagation Problems in Infinite Media
Chapter 22. Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms
Chapter 23. On the Stochastic Integral Equation of Fredholm Type
Chapter 24. An Approach to Constrained Equations and Strange Attractors
Chapter 25. On the Existence of Progressive Waves in the Flow of Perfect Fluid around a Circle
Chapter 26. On Laminar Boundary Layers with Suction
Chapter 27. Initial Value Problem for Kac’s Model of the Boltzmann Equation
Chapter 28. The Initial Value Problem for the Equations of the Motion of Compressible Viscous Fluid with Some Slip Boundary Condition
Index