UK Nonlinear News, August 2000.


Article: Blowup in Reaction-Diffusion Systems with Dissipation of Mass

Michel Pierre and Didier Schmitz. Blowup in Reaction-Diffusion Systems with Dissipation of Mass. SIAM Review Volume 42(1), March 2000, pages 93-106.

Abstract: We prove possible blowup in finite time of the solutions to reaction-diffusion systems which preserve nonegativity and for which the total mass of the components is nonincreasing in time (two natural properties in applications). This is done by presenting explicit counterexamples constructed with the help of formal computation software. Several partial results of global existence had been obtained previously in the literature. Our counterexamples explain a posteriori why extra conditions were needed. Negative results of independent interest are also provided as a by-product for linear parabolic equations in nondivergence form and with discontinuous coefficients and for nonlinear Hamilton-Jacobi evolution equations.

Article: Stochastic Spatial Models

Rick Durrett. Stochastic Spatial Models. SIAM Review Volume 41(4), December 1999.

Abstract: In the models we will consider, space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites. Our main aim here is to explain an idea of Durrett and Levin (1994): the behaviour of these models can be predicted from the properties of the mean field ODE, i.e., the equations for the densities of the various types that result from pretending that all sites are always independent. We will illustrate this picture through a discussion of eight families of examples from statistical mechanics, genetics, population biology, epidemiology, and ecology. Some of our findings are only conjectures based on simulation, but in a number of cases we are able to prove results for systems with "fast stirring" by exploiting connections between the spatial model and an associated reaction diffusion equation.

New issue of Dynamic Notes (2000.01) released

The SIAM Activity Group on Dynamical Systems has recently released a new issue of their newsletter Dynamic Notes. It is available from their new web site:

International Journal of Nonlinear Sciences and Numerical Simulation - Contents list: Volume 1, Number 2, 2000

Review Article
Review of Virtual Distortion Method and Its Applications to Fast Redesign and Sensitivity Analysis
Jan Holnicki-Szulc, Tomasz Bielecki71
Technical Papers
Optic Discrete Breathers in Euclidean Invariant Systems
R.S.MacKay 99
Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank
Oleg S. Imarchenko
Dynamics of Stochastic Layers in Nonlinear Hamiltonian Systems
Albert C.J. Luo and Ray P.S. Han
A Classical Variational Model for Micropolar Elastodynamics
Ji-Huan He133
A Variational Model for Micropolar Fluids in Lubrication Journal Bearing
Ji-Huan He139
Book Review
Preprinciples of Mechanics (Veljko A. Vujicic)
Katica (Stevanovic) Hedrih143

Source: Wen CHEN (

NONLINEARITY Contents list: Volume 13(4), July 2000

Pages: 973--1424

973 V. Afraimovich and B. Fernandez
Topological properties of linearly coupled expanding map lattices.
995 H. Sumi
Skew product maps related to finitely generated rational semigroups
1021 J. Palaci\'an and P. Yanguas
Reduction of polynomial Hamiltonians by the construction of formal integrals
1055 L. Flatto and J.C. Lagarias
The lap-counting and zeta functions of the tent map
1073 A. Ramani, Y. Ohta and B. Grammaticos
Discrete integrable systems from continuous Painlev\'e equations through limiting procedures
1087 S. Yakovenko
On zeros of functions from Bernstein classes
1095 G. Olivar, E. Fossas and C. Batlle
Bifurcations and chaos in converters. Discontinuous vector fields and singular Poincar\'e maps
1123 V. Zharnitsky
Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi--Ulam problem
1137 A. Alonso Izquierdo, M.A. Gonz\'alez Le\'on and J. Mateos Guilarte
Kinks from dynamical systems: domain walls in a deformed O(N) linear sigma model
1171 M. Dellnitz, G. Froyland and S. Sertl
On the isolated spectrum of the Perron--Frobenius operator
1189 C. Fermanian Kammerer and H. Zaag
Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation
1217 T. Ioannidou
SU(N) skyrmions from instantons
1227 N. Ju
The H1 compact global attractor for the solutions to the Navier--Stokes equations in two-dimensional unbounded domains
1239 J-F Collet and T. Goudon
On solutions of the Lifshitz--Slyozov model
1263 P. Collet, S. Mart\'{rm i} nez and V. Maume-Deschamps
On the existence of conditionally invariant probability measures in dynamical systems
1275 M. Degli Esposti, G. Del Magno and M. Lenci
Escape orbits and ergodicity in infinite step billiards
1293 P.C. Matthews and S.M. Cox
Pattern formation with a conservation law
1321 K Josi\'c
Synchronization of chaotic systems and invariant manifolds
1337 Yu Ilyashenko
Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
1343 G. Grammel
On the Van-der-Pol oscillator with noisy nonlinearity
1357 B. Sandstede, S. Balasuriya, C.K.R.T. Jones and P. Miller
Melnikov theory for finite-time vector fields
1379 F. Cantrijn, M. de Le\'on, J.C. Marrero and D. Mart\'{rm i}n de Diego
On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework
1411 P. Bizo\'n, T. Chmaj and Z. Tabor
Dispersion and collapse of wave maps

Source: Elizabeth Martin.

New Journal: International Journal of Nonlinear Modelling in Science and Engineering

Editorial by Dr. Ji-Huan He ( Shanghai University, Shanghai 200072)

Nonlinear phenomena appear everywhere in our daily life and in our scientific work, and today they represent one of the most important fields of research in science and technology. There exist innumerable hidden pearls in various nonlinear phenomena, these pearls can only be found by proper mathematical modelling, which may be simple and beautiful, or complex and exciting.

We feel that there is an urgent need for an International Journal of Nonlinear Modelling in Science and Engineering. The aim of this journal is to bring to the fore the many new and exciting nonlinear mathematical modelling applications in science and engineering, thereby capturing both the interest and imagination of the wider communities in various fields, such as in mathematics, physics, chemistry, earth science, computational science, biologics, economics, and nanotechnolgy. We hope by studying or improving the proposed modelling, new branches of science will occur, for example, nano-mathematics, nano-chemistry, nano-physics, nano-biotechnology and the like.

The emphasis of this journal, therefore, is placed on how to establish a proper nonlinear modelling for a real-life nonlinear problem, to search for pearls through complex phenomena by numerical or analytical solution. The numerical techniques for some special nonlinear modellings, for example, nonlinear fractional differential equations, are also welcome.

To make the journal accessible to a broad audience, the authors will, in the first Issue, present an overview of the current status of their fields with a speculative outlook on what are to come out in the future.

We are now seeking financial support from all sectors, and nominations of contributing editors specialized in various fields are mostly welcome. We cordially invite universities and institutes worldwide to sponsor this new journal.

My address is _______________________________________________________________

Source: Wen Chen (

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