The book is an account on recent advances in elliptic and
parabolic problems and related equations, including general quasi-linear
equations, variational structures, Bose-Einstein condensate,
Chern亡imons model, geometric shell theory and stability in
fluids. It presents very up-to-date research on central issues of
these problems such as maximal regularity, bubbling, blowing-up,
bifurcation of solutions and wave interaction. The contributors
are well known leading mathematicians and prominent young
researchers.
Contents:
Maximal Regularity and Quasilinear Parabolic Boundary Value
Problems (H Amann)
Remarks on the Two and Three Membranes Problem (J-F Rodrigues et
al.)
Bubbling and Criticality in Two and Higher Dimensions (M del Pino
& M Musso)
Blow Up Solutions for a Liouville Equation with Singular Data (P
Esposito)
Problems in Unbounded Cylindrical Domains (P Guidotti)
Entire Solutions of Some Reaction-Diffusion on Equations (J-S Guo)
Some Abelian Gauge Field Theories in the Self-dual and Nonself-dual
Cases (J Han & N Kim)
Ginzburg-Landau Equations on Non-uniform Media (S Kosugi)
Finding the Elasticae by Means of Geometric Gradient Flows (C-C
Lin & H R Schwetlick)
Free Work Identity and Nonlinear Instability in Fluids with Free
Boundaries (M Padula)
Complete and Energy Blow-up in Superlinear Parabolic Problems (P
Quittner)
Non-stabilizing Solutions for a Supercritical Semilinear
Parabolic Equation (E Yanagida)
and other papers
Readership: Graduate students and researchers in partial
differential equations, mathematical physics and mechanics.
284pp Pub. date: Feb 2005
ISBN 981-256-189-7
The book presents a collection of results pertaining to the partial regularity
of solutions to various variational problems, all of which are connected
to the Dirichlet energy of maps between Riemannian manifolds, and thus
related to the harmonic map problem. The topics covered include harmonic
maps and generalized harmonic maps; certain perturbed versions of the harmonic
map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert)
equation. Since the methods in regularity theory of harmonic maps are quite
subtle, it is not immediately clear how they can be applied to certain
problems that arise in applications. The book discusses in particular this
question.
Contents:
Analytic Preliminaries
Harmonic Maps
Almost Harmonic Maps
Evolution Problems
Readership: Researchers and graduate students in analysis and
differential equations.
192pp Pub. date: Feb 2005
ISBN 981-256-085-8
Cosmic evolution leads from symmetry to complexity by symmetry
breaking and phase transitions. The emergence of new order and
structure in nature and society is explained by physical,
chemical, biological, social and economic self-organization,
according to the laws of nonlinear dynamics. All these dynamical
systems are considered computational systems processing
information and entropy. Are symmetry and complexity only useful
models of science or are they universals of reality? Symmetry and
Complexity discusses the fascinating insights gained from
natural, social and computer sciences, philosophy and the arts.
With many diagrams and pictures, this book illustrates the spirit
and beauty of nonlinear science. In the complex world of
globalization, it strongly argues for unity in diversity.
Contents:
Symmetry and Complexity in Early Culture and Philosophy
Symmetry and Complexity in Mathematics
Symmetry and Complexity in Physical Sciences
Symmetry and Complexity in Chemical Sciences
Symmetry and Complexity in Life Sciences
Symmetry and Complexity in Economic and Social Sciences
Symmetry and Complexity in Computer Science
Symmetry and Complexity in Philosophy and Arts
Readership: Upper-level undergraduates, graduate students,
researchers, academics, and professionals in interdisciplinary
sciences.
320pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-192-7
This volume presents a comprehensive collection of Wang Yuan’s
original important papers which are not available elsewhere,
since the majority of the papers were published in China.
Covering both pure number theory and applied mathematics, this
book is important for understanding Wang Yuan’s academic career
and also the development of Chinese mathematics in recent years,
since Wang Yuan’s work has a wide-ranging influence in China.
Wang Yuan is a professor and academician of the Chinese Academy
of Sciences. He received his Doctorship from Hong Kong Baptist
University. He has published 70 papers and ten books.
Contents:
Analytic Number Theory: Goldbach Conjecture, Least Primitive Root
Diophantine Analysis: Small Solutions for a System of Diophantine
Inequalities and Equations
Applied Mathematics: Hua?Wang Method on Numerical Integration,
and Experimental Designs
Readership: Researchers, teachers and graduate students in number
theory, numerical analysis and statistics.
550pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-197-8
Seminaires et Congres 9 (2004), xviii+208 pages
Resume :
Les 17 et 18 juin 2002, le Laboratoire de Mathematiques de Nantes a organise des journees mathematiques a la memoire de Jean Leray. A cette occasion le Laboratoire a pris le nom de Laboratoire Jean Leray . Ce volume commence par l'expose d'Yves Meyer qui retrace le parcours scientifique de Jean Leray. Les exposes suivants sont des articles illustrant la plupart des aspects des travaux de J. Leray et montrant l'etendue du spectre de son ?uvre. Le lecteur pourra facilement deviner auquel des trois volumes des ?uvres completes se rapporte chacun des articles.
Mots clefs : Equation de Navier-Stokes, faisceaux, analyse microlocale, hydrodynamique, probleme de Neumann-Kelvin, phase stationnaire, singularites d'hypersurface, problemes de Cauchy, fonctions de Green, residus, courbes pseudoholomorphes, operades, fluides incompressibles, developpements asymptotiques
Abstract:
Proceedings of the colloquium dedicated to the memory of Jean Leray, Nantes, 2002
On the 17th and 18th of June 2002 the Laboratory of Mathematics of Nantes University (supported by CNRS) has organized a meeting to celebrate the memory of Jean Leray. At this opportunity the Laboratory took the name Laboratoire Jean Leray . This volume starts with the lecture by Yves Meyer, which relates the scientific life of Jean Leray. The following lectures are papers illustrating most aspects of scientific works of J. Leray and showing up the wide spectrum of his work. The reader will easily guess to which of the three volumes of the collected papers each paper is linked.
Key words: Navier-Stokes equation, sheaves, microlocal analysis, hydrodynamics, Neumann-Kelvin problem, stationary phase, hypersurface singularity, Cauchy problem, Green function, residues, pseudoholomorphic curve, operade, incompressible fluid, asymptotic expansion
ISBN : 2-85629-160-0