Patterns and Waves book cover

Patterns and Waves

Qualitative Analysis of Nonlinear Differential Equations

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.

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Published: January 1986

Imprint: North-holland

ISBN: 978-0-444-70144-2

Contents

  • The Soul of Mathematics (P.D. Lax). Part I. Hyperbolic Partial Differential Equations. Flow Problems. Reaction-Diffusion Equations. Chaos and Fractals. Numerical Analysis & Computations. Contributors: H. Fujii, M. Hata, Y. Hosono, N. Iwasaki, Y. Kan-on, M. Mimura, S. Mizohata, T. Nishida, Y. Nishiura, T. Nogi, M. Tabata, S. Ukai, S. Ushiki.Part II. Positive Solutions to Some Semilinear Elliptic Equations in L1(Rn) (M. Arai and A. Nakaoka). On the Vlasov-Poisson Limit of the Vlasov-Maxwell Equation (K. Asano and S. Ukai). A Discrete Model for Spatially Aggregating Phenomena (T. Ikeda). A Note on the Blowing-Up Problem of a Certain System of Nonlinear Parabolic Equations (N. Itaya). L'équation de Kadomtsev-Petviashvili approchant les ondes longues de surface de l'eau en écoulement trois-dimensionnel (T. Kano). Application of an Iteration Scheme to the Analysis of Incompressible or Nearly Incompressible Media (F. Kikuchi). On a Local Existence Theorem for the Evolution Equation of Gaseous Stars (T. Makino). Fundamental Solution of the Linearized System for the Exterior Stationary Problem of Compressible Viscous Flow (A. Matsumara). Nonlocal Advection Effect on Bistable Reaction-Diffusion Equations (M. Mimura, D. Terman and T. Tsujikawa). On Small Data Scattering for Some Nonlinear Wave Equations (K. Mochizuki and T. Motai). The Near-Field Finite Difference Approximation for Wave Propagation Problems in Infinite Media (T.-T. Nakagawa). Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms (M. Nakao). On the Stochastic Integral Equation of Fredholm Type (S. Ogawa). An Approach to Constrained Equations and Strange Attractors (H. Oka and H. Kokubo). On the Existence of Progressive Waves in the Flow of Perfect Fluid around a Circle (H. Okamoto and M. Shōji). On Laminar Boundary Layers with Suction (T. Shirota). Initial Value Problem for Kac's Model of the Boltzmann Equation (Y. Shizuta and H. Nishiyama). The Initial Value Problem for the Equations of the Motion of Compressible Viscous Fluid with Some Slip Boundary Condition (A. Tani). Index.

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