This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.

The First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997. Researchers from around the world attended-including representatives from the US, Canada, and the Netherlands-but the majority of the speakers hailed from China and Hong Kong. This volume contains the plenary lectures and invited talks presented at that conference, and provides an excellent view of the research on differential equations being carried out in China. Most of the subjects addressed arose from actual applications and cover ordinary and partial differential equations. Topics include:

This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments. Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.

This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.

In 1975 the Marcel Grossmann Meetings were established by Remo Ruffini and Abdus Salam to provide a forum for discussion of recent advances in gravitation, general relativity, and relativistic field theories. In these meetings, which are held once every three years, every aspect of research is emphasized - mathematical foundations, physical predictions, and numerical and experimental investigations. The major objective of these meetings is to facilitate exchange among scientists, so as to deepen our understanding of the structure of space-time and to review the status of both the ground-based and the space-based experiments aimed at testing the theory of gravitation.The Marcel Grossmann Meetings have grown under the guidance of an International Organizing Committee and a large International Coordinating Committee. The first two meetings, MG1 and MG2, were held in Trieste (1975, 1979). A most memorable MG3 (1982) was held in Shanghai and represented the first truly international scientific meeting in China after the so-called Cultural Revolution. Three years later MG4 was held in Rome (1985). It was at MG4 that ';astroparticle physics'; was born.MGIXMM was organized by the International Organizing Committee composed of D Blair, Y Choquet-Bruhat, D Christodoulou, T Damour, J Ehlers, F Everitt, Fang Li Zhi, S Hawking, Y Ne'eman, R Ruffini (chair), H Sato, R Sunyaev, and S Weinberg. Essential to the organization was an International Coordinating Committee of 135 members from scientific institutions of 54 countries. MGIXMM was attended by 997 scientists of 69 nationalities. It took place on 2-8 July 2000 at the University of Rome, Italy. The scientific programs included 60 plenary and review talks, as well as talks in 88 parallel sessions. The three volumes of the proceedings of MGIXMM present a rather authoritative view of relativistic astrophysics, which is becoming one of the priorities in scientific endeavour. The papers appearing in these volumes cover all aspects of gravitation, from mathematical issues to recent observations and experiments. Their intention is to give a complete picture of our current understanding of gravitational theory at the turn of the millennium.The Marcel Grossmann Individual Awards for this meeting were presented to Cecille and Bryce DeWitt, Riccardo Giacconi and Roger Penrose, while the Institutional Award went to the Solvay Institute, accepted on behalf of the Institute by Jacques Solvay and Ilya Prigogine. The acceptance speeches are also included in the proceedings.

This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.

Annotation. Proceedings from the First International Conference on Inverse Problems, Recent Theoretical Development and Numerical Approaches, held at the City University of Hong Kong from January 9-12, 2002.

Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.