Joint Australian-Taiwanese Workshop on Analysis and Applications

(Brisbane, March 1997)

Volume 37 in the Proceedings of the Centre for Mathematics and its Applications

Preface

This volume contains the proceedings of the joint Australian-Taiwanese "Workshop on Analysis and Applications" held at The University of Queensland from March 31 to April 04, 1997. The Worskshop brought together researchers from Australia and Taiwan working in harmonic analysis, nonlinear partial differential equations, dynamical systems and control theory, geometric and physical applications, and computational mathematics and its applications. Many of the participants established new research collaborations through this opportunity to interact with colleagues from these related although different areas. We hope this workshop will be the first of many, strengthening the mathematics communities in each country and deepening the bonds of friendship between them.

The Workshop was supported by the National Science Council of Taiwan and the Australian Department of Industry, Science and Technology's Bilateral Science and Technology Collaboration program.

Contributions for the proceedings were sought from all Workshop delegates and all papers received were carefully refereed. One can see from the contributions the enormous range and depth of mathematical research currently being carried out in Australia and Taiwan.

The Workshop was organised by Fon-Che Liu of Academia Sinica, Neil Trudinger of the Australian National University, Hung-Ju Kuo of Chung-Hsing University and Bevan Thompson of The University of Queensland. A "Conference on Analysis and Applications" was held at The University of Queensland during the same period. Both the Workshop and the Conference were a great success with first rate Scientific Programs, great weather, and many friendly, outstanding, enthusiastic colleagues contributing to a stimulating research environment. The organisers would like to thank all participants for their role in the success of the venture. Particular thanks are due to the Treasurer, Jan Chabrowski, the Web Master, Elliot Tonkes, and the Secretary, Tim Cranny, for their extensive help in the smooth running of the Workshop and the Conference.

Tim Cranny & Bevan Thompson
(Editors)

Contents

Preface	i
Conference Delegates	iii
Some Slightly Subcritical or Slightly Supercritical Problems E.N.Dancer	1
Some Lusin Properties of Functions Fon-Che Liu	7
The Lp Boundedness of Riesz Transforms Associated with Divergence Form Operators Xuan Thinh Dong and Alan McIntosh	15
Cellular Neural Networks: Pattern Formation and Spatial Chaos Jonq Juang and Song-Sun Lin	27
A Configuration Space for Solutions of Maxwell's Equations Robert Bartnik	39
Structural Inequalities Method for Uniqueness Theorems for the Minimal Surface Equation Jenn-Fang Hwang	47
Asymptotic Solutions of Scientific Interest Roger J. Hosking	53
Stability and Shadowing in Convex Discrete-Time Systems Phil Diamond and Alexei Pokrovski	63
Chaotic Vibration of the Infinite Dimensional Harmonic Oscillator due to a Self-Excitation Boundary Condition, Part I: controlled Hysteresis Goong Chen, Sze-Bi Hsu and Jianxin Zhuo	75
A Parallel Matrix-Free Implementation of a Runge-Kutta Code Kevin Burrage, Craig Eldershaw and Roger Sidje	83
Balancing of Diffusion Partial Differential Equations Fang-Bo Yeh	89
Spectral Flow in Breuer-Fredholm Modules A.L.Carey and John Phillips	99
On the Blow-Up Behaviour of Solutions of Scalar Curvature Equations and its Application Chang-Shou Lin	109
Mean Curvature Evolution of Spacelike Hypersurfaces Klaus Ecker	119
Interpolating Wavelets and Difference Wavelets I-Liang Chern	133