Patterns and Waves: Qualitative Analysis of Nonlinear Differential Equations

✍ Scribed by Takaaki Nishida, Masayasu Mimura and Hiroshi Fujii (Eds.)

• Publisher: Elsevier Science Ltd
• Year: 1986
• Tongue: English
• Leaves: 709
• Series: Studies in Mathematics and Its Applications 18
• 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

Content:
Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vi-vii
Takaaki Nishida, Masayasu Mimura, Hiroshi Fujii

The Soul of Mathematics
Pages viii-ix
Peter D. Lax

On Weakly Hyperbolic Equations with Constant Multiplicities Original Research Article
Pages 1-10
Sigeru Mizohata

Strongly Hyperbolic Equations and their Applications Original Research Article
Pages 11-36
Nobuhisa Iwasaki

Solutions of the Boltzmann Equation Original Research Article
Pages 37-96
Seiji Ukai

Equations of Motion of Compressible Viscous Fluids Original Research Article
Pages 97-128
Takaaki Nishida

Predation-Mediated Coexistence and Segregation Structures Original Research Article
Pages 129-155
Masayasu Mimura, Yukio Kan-on

On the Structure of Multiple Existence of Stable Stationary Solutions in Systems of Reaction-Diffusion Equations Original Research Article
Pages 157-219
Hiroshi Fujii, Yasumasa Nishiura, Yuzo Hosono

Chaotic Phenomena and Fractal Objects in Numerical Analysis Original Research Article
Pages 221-258
Shigehiro Ushiki

Fractals in Mathematics Original Research Article
Pages 259-278
Masayoshi Hata

Parallel Computation Original Research Article
Pages 279-318
Tatsuo Nogi

A Theoretical and Computational Study of Upwind-Type Finite Element Methods Original Research Article
Pages 319-356
Masahisa Tabata

Positive Solutions to Some Semilinear Elliptic Equations in L¹(Rⁿ) Original Research Article
Pages 357-367
Masaharu Arai, Akira Nmakaoka

On the Vlasov-Poisson Limit of the Vlasov-Maxwell Equation Original Research Article
Pages 369-383
Kiyoshi Asano, Seiji Ukai

A Discrete Model for Spatially Aggregating Phenomena Original Research Article
Pages 385-418
Tsutomu Ikeda

A Note on the Blowing-up Problem of a Certain System of Nonlinear Parabolic Equations Original Research Article
Pages 419-429
Nobutoshi Itaya

L'équation de Kadomtsev-Petviashvili approchant les ondes longues de surface de l'eau en écoulement trois-dimensionnel Original Research Article
Pages 431-444
Par Tadayoshi Kano

Application of an Iteration Scheme to the Analysis of Incompressible or Nearly Incompressible Media Original Research Article
Pages 445-458
Fumio Kikuchi

On a Local Existence Theorem for the Evolution Equation of Gaseous Stars Original Research Article
Pages 459-479
Tetu Makino

Fundamental Solution of the Linearized System for the Exterior Stationary Problem of Compressible Viscous Flow Original Research Article
Pages 481-505
Akitaka Matsumura

Nonlocal Advection Effect on Bistable Reaction-Diffusion Equations Original Research Article
Pages 507-542
Masayasu Mimura, David Terman, Tohru Tsujikawa

On Small Data Scattering for Some Nonlinear Wave Equations Original Research Article
Pages 543-560
Kiyoshi Mochizuki, Takahiro Motai

The Near-field Finite Difference Approximation for Wave Propagation Problems in Infinite Media Original Research Article
Pages 561-582
Tomoyasu-Taguti Nakagawa

Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms Original Research Article
Pages 583-596
Mitsuhiro Nakao

On the Stochastic Integral Equation of Fredholm Type Original Research Article
Pages 597-605
Shigeyoshi Ogawa

An Approach to Constrained Equations and Strange Attractors Original Research Article
Pages 607-630
Hiroe Oka, Hiroshi Kokubu

On the Existence of Progressive Waves in the Flow of Perfect Fluid around a Circle Original Research Article
Pages 631-644
Hisashi Okamoto, Mayumi Shōji

On Laminar Boundary Layers with Suction Original Research Article
Pages 645-662
Taira Shirota

Initial Value Problem for Kac's Model of the Boltzmann Equation Original Research Article
Pages 663-673
Yasushi Shizuta, Hideko Nishiyama

The Initial Value Problem for the Equations of the Motion of Compressible Viscous Fluid with Some Slip Boundary Condition Original Research Article
Pages 675-684
Atusi Tani

Index
Pages 685-692