Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.

The International Conference devoted to Theory, Numerics and Applications of Hyperbolic Problems, HYP2012, was held in Padova on June 24–29, 2012. The conference was the fourteenth in a highly successful series of bi-annual meetings that has become one of the most important international events in Applied Mathematics. The volume contains more than 110 contributions that were presented in this conference, including plenary presentations by C. De Lellis, E. Feireisl, N. Masmoudi, S. Mishra, G. Russo, J. Sethian, E. Zuazua, and a contribution by the keynote speaker J. Glimm. These contributions cover a wide range of topics. A very partial list includes: new methods for constructing turbulent solutions to multi-dimensional systems of conservation laws based on Baire category, transport equations with non-Lipschitz velocity fields, relative entropy functionals and the stability of fluid systems, numerical methods for hyperbolic systems with stiff relaxation terms and for multiphase flow, new advances in homogenization theory, optimal sensor location for solutions to multidimensional wave equations, singularities in general relativity. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.

The contributions collected in this volume cover a wide range of topics.Some of these represent the latest developments on classicalmulti-dimensional problems, dealing with shock reflections and withthe stability of vortices and boundary layers. Other contributionsprovide sharp results on the structure and regularity of solutions toconservation laws, or discuss the fine line between well-posedness andill-posedness for transport equations with rough coefficients, and for theequations of inviscid fluid flow. Further progress is reported at theinterface between hyperbolic and kinetic models, including thehydrodynamic limit of the Boltzmann equation. Kinetic andmacroscopic models for collective dynamics of many-body systems,which have attracted much interest in recent years, are also covered inthis volume. Finally, a large number of papers are devoted to advancesin computational methods, with diverse applications such as: submarineavalanches, tsunami waves, chemically reacting flows, solitary waves,gas flow on a network of pipelines, traffic flow with multiple types ofvehicles, etc.

The following chapters summarize lectures given in March 2001 during the summerschool on Hyperbolic Partial Differential Equations which took place at the Technical University of Hamburg-Harburg in Germany. This type of meeting is originally funded by the Volkswa­ genstiftung in Hannover (Germany) with the aim to bring together well-known leading experts from special mathematical, physical and engineering fields of interest with PhD­ students, members of Scientific Research Institutes as well as people from Industry, in order to learn and discuss modern theoretical and numerical developments. Hyperbolic partial differential equations play an important role in various applications from natural sciences and engineering. Starting from the classical Euler equations in fluid dynamics, several other hyperbolic equations arise in traffic flow problems, acoustics, radiation transfer, crystal growth etc. The main interest is concerned with nonlinear hyperbolic problems and the special structures, which are characteristic for solutions of these equations, like shock and rarefaction waves as well as entropy solutions. As a consequence, even numerical schemes for hyperbolic equations differ significantly from methods for elliptic and parabolic equations: the transport of information runs along the characteristic curves of a hyperbolic equation and consequently the direction of transport is of constitutive importance. This property leads to the construction of upwind schemes and the theory of Riemann solvers. Both concepts are combined with explicit or implicit time stepping techniques whereby the chosen order of accuracy usually depends on the expected dynamic of the underlying solution.

The Ninth EPSRC Numerical Analysis Summer School was held at the Uni­ versity of Durharn, UK, from the 10th to the 21st of July 2000. This was the first of these schools to be held in Durharn, having previously been hosted, initially by the University of Lancaster and latterly by the University of Leicester. The purpose of the summer school was to present high quality in­ structional courses on topics at the forefront of numerical analysis research to postgraduate students. Eminent figures in numerical analysis presented lectures and provided high quality lecture notes. At the time of writing it is now more than two years since we first con­ tacted the guest speakers and during that period they have given significant portions of their time to making the summer school, and this volume, a suc­ cess. We would like to thank all six of them for the care which they took in the preparation and delivery of their lectures.

Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.

Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame­ ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ­ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor­ respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe­ nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in­ duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu­ merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con­ tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce­ nario, mode-interactions and impact of boundary conditions.

This book describes the water, wildlife, and livelihood of Tonle Sap Lake and its basin in Cambodia, the largest freshwater lake in Southeast Asia. It comprehensively elucidates the processes underlying the dynamic, productive, and unique ecosystem, covering the major environmental and administrative components such as climate, water flow and storage, sediment, nutrient, flora, fauna, floating villages, management, and governance. Anthropogenic impacts including climate change on the lake are also highlighted.

This book describes the water, wildlife, and livelihood of Tonle Sap Lake and its basin in Cambodia, the largest freshwater lake in Southeast Asia. It comprehensively elucidates the processes underlying the dynamic, productive, and unique ecosystem, covering the major environmental and administrative components such as climate, water flow and storage, sediment, nutrient, flora, fauna, floating villages, management, and governance. Anthropogenic impacts including climate change on the lake are also highlighted.

Fracture mechanics has established itself as an important discipline of growing interest to those working to assess the safety, reliability and service life of engineering structures and materials. In order to calculate the loading situation at cracks and defects, nowadays numerical techniques like finite element method (FEM) have become indispensable tools for a broad range of applications.