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Hyperbolic Problems: Theory, Numerics, Applications
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.
Handbook of Mathematical Fluid Dynamics
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Control Methods in PDE-Dynamical Systems
While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respecti...
Hyperbolic Problems: Theory, Numerics and Applications
The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.
Nonlinear Conservation Laws and Applications
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of vis...
Numerical Methods for Conservation Laws
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than ...
Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.
Hyperbolic Problems: Contributed talks
The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, ``HYP2008'', was held at the University of Maryland from June 9-13, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. This book, the second in a two-part volume, contains more than sixty articles based on contributed talks given at the conference. The articles are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ``hyperbolic PDEs''. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.
