springer.de/buchhandel Springer News 11/12/2007 Mathematik 39 R. P. Agarwal, Florida Institute of Technology, L. Ambrosio, L. Caffarelli, M. G. Crandall, L. C. Evans, C. Bardos, Université Denis Diderot, Paris, France; Melbourne, FL, USA; D. O‘Regan, National University N. FuscoB. Dacorogna, P. Marcellini (Eds.) A. Fursikov, Moscow State University, Institute of of Ireland, Galway, Ireland Numerical Mathematics RAS (Eds.) Calculus of Variations and An Introduction to Ordinary Non-Linear Partial Differential Instability in Models Differential Equations Equations Connected with Fluid Flows I Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005 Ordinary differential equations serve as mathemat- The notions of stability and instability play a very ical models for many exciting real world problems. With contributions by: E. Mascolo important role in mathematical physics and, in Rapid growth in the theory and applications of particular, in mathematical models of fluids flows. differential equations has resulted in a continued Currently, one of the most important roblems in interest in their study by students in many disci- This volume provides the texts of lectures given by this area is to describe different kinds of instability, plines. L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, to understand their nature, and also to work out Key Features of this textbook: Organizes material N. Fusco at the Summer course held in Cetraro methods for recognizing whether a mathematical around theorems and proofs; Comprises of 42 (Italy) in 2005. These are introductory reports on model is stable or instable. In the current volume, class-tested lectures that effectively convey the current research by world leaders in the fields of Claude Bardos and Andrei Fursikov, have drawn subject in easily manageable sections; presentation calculus of variations and partial differential equa- together an impressive array of international is driven by detailed examples that illustrate how tions. The topics discussed are transport equations contributors to present important recent results the subject works; includes numerous exercise for non smooth vector fields, homogenization, and perspectives in this area. The main topics sets, with an “answers and hints” section; provides viscosity methods for the infinite Laplacian, weak covered are devoted to mathematical aspects of the a background and history of the subject through KAM theory and geometrical aspects of symmetri- theory but some novel schemes used in applied interesting preliminary lectures; the rich array zation. Besides there is also an historical overview mathematics are also presented. of topics allows for flexibility in developing the of all CIME courses on the calculus of variations subject beyond the basics. and partial differential equations contributed by Features Elvira Mascolo. 7 A unique collection of papers of leading From the contents specialists presenting the very recent results and Solvable Differential Equations.- Second Order Contents advantages in the main directions of stability Differential Equations.- Preliminaries to Series Preface by Bernard Dacorogna and Paolo theory in connection with fluid flows Solutions.- Solution at an Ordinary Point.- Solu- Marcellini.- Luigi Ambrosio: Transport Equation tion at a Singular Point.- Solution at a Singular and Cauchy Problem for Non-Smooth Vector Contents Point (Contd.).- Legendre Polynomials and Fields.- Luis Caffarelli and Luis Silvestre: Issues in Preface, Claude Bardos and Andrei Fursikov.- Functions.- Chebyshev, Hermite and Laguerre Homogenization for Problems with non Diver- Solid Controllability in Fluid Dynamics, Andrey Polynomials.- Bessel Functions.- Hypergeometric gence Structure.- Michael G. Crandall: A Visit with Agrachev and Andrey Sarychev.- Analyticity of Functions.- Piecewise Continuous and Periodic the 8-Laplace Equation.- Lawrence C. Evans: Weak Periodic Solutions of the 2D Boussinesq System, Functions.- Orthogonal Functions and Polyno- KAM Theory and Partial Differential Equations.- Maxim Arnold.- Nonlinear Dynamics of a System mials.- Orthogonal Functions and Polynomials Nicola Fusco: Geometrical Aspects of Symmetriza- of Particle-Like Wavepackets, Anatoli Babin and (contd.).- Boundary Value Problems.- Boundary tion.- Elvira Mascolo: CIME Courses on Partial Aleksander Figotin.- Attractors for Nonautono- Value Problems (contd.).- Green’s Functions.- Differential Equations and Calculus of Variations. mous Navier–Stokes System and Other Partial Regular Perturbations.- Singular Perturba- Differential Equations, Vladimir Chepyzhov and tions.- Sturm-Liouville Problems.- Eigenfunction Fields of interest Mark Vishik.- Recent Results in Large Amplitude Expansions.- Eigenfunction Expansions (contd.).- Calculus of Variations and Optimal Control; Opti- Monophase Nonlinear Geometric Optics, Chris- Convergence of the Fourier Series.- Convergence mization; Partial Differential Equations tophe Cheverry. of the Fourier Series (contd.).- Fourier Series Solutions of Ordinary Differential Equations.- Target groups Fields of interest Partial Differential Equations.- First Order Partial Researchers and graduate students Analysis; Calculus of Variations and Optimal Differential Equations. Control; Optimization; Computational Math- Type of publication ematics and Numerical Analysis Fields of interest Collection of essays Ordinary Differential Equations; Partial Differen- Target groups tial Equations; Appl. Mathematics/Computational Researches, specialists in calculus, mathematical Methods of Engineering analysis, theory of PDEs, optimal control, fluid mechanics, theoretical physics, computational Target groups mathematics, and also related disciplines Senior undergraduates, graduate students, math- ematicians Type of publication Contributed volume Type of publication Graduate/Advanced undergraduate textbook Due December 2007 Due February 2008 Due January 2008 2008. XII, 202 p. (Lecture Notes in Mathematics / 2008. Approx. 400 p. (International Mathematical Series, 2008. Approx. 335 p. 8 illus. (Universitext) Softcover Fondazione C.I.M.E., Firenze, Volume 1927) Softcover Volume 6) Hardcover 7 approx. * € (D) 49,43 | € (A) 50,82 | sFr 80,50 7 approx. * € (D) 42,75 | € (A) 43,95 | sFr 70,00 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 9<HTLDTH=hbchfi>ISBN 978-0-387-71275-8 9<HTOFPA=hfjbdd>ISBN 978-3-540-75913-3 9<HTLDTH=hfcbgh>ISBN 978-0-387-75216-7 40 Mathematik Springer News 11/12/2007 springer.de/buchhandel C. Bardos, Université Denis Diderot, Paris, France; C. Bardos, Université Denis Diderot, Paris, France; S. Benzoni-Gavage, Université Claude Bernard Lyon A. Fursikov, Moscow State University, Institute of A. Fursikov, Moscow State University, Institute of I, France; D. Serre, Ecole Normale Supérieure, Lyon, Numerical Mathematics RAS (Eds.) Numerical Mathematics RAS (Eds.) France (Eds.) Instability in Models Instability in Models Hyperbolic Problems: Theory, Connected with Fluid Flows II Connected with Fluid Flows Numerics, Applications Set Proceedings of the XIth International Conference on Hyperbolic Problems held Stability is a very important property of math- in Ecole Normale Supérieure, Lyon, ematical models simulating physical processes The advantages of the study of the stability and July 17-21, 2006 which provides an adequate description of the instability of models in fluid mechanics are process. Starting from the classical notion of the presented by world-recognized specialists in math- well-posedness in the Hadamard sense, this notion ematical analysis, PDEs, optimal control, etc. was adapted to different areas of research and at The two volumes are available separately, or This volume contains papers that were presented at present is understood, depending on the physical together at a reduced price for the two-volume HYP2006, the eleventh international Conference problem under consideration, as the Lyapunov set. See the entries for the individual volumes for on Hyperbolic Problems: Theory, Numerics and stability of stationary solutions, stability of speci- details of the coverage of each volume. Applications held at the Ecole Normale Supérieure fied initial data, stability of averaged models, etc. de Lyon, France, July 17-21, 2006. This biennial The stability property is of great interest for Features series of conferences has become one of the most researchers in many fields such as mathematical 7 A unique collection of papers of leading important international events in Applied Math- analysis, theory of partial differential equa- specialists presenting the very recent results and ematics. As computers became more and more tions, optimal control, numerical analysis, fluid advantages in the main directions of stability powerful, the interplay between theory, model- mechanics, etc. theory in connection with fluid flows ling, and numerical algorithms gained consider- able impact, and the scope of HYP conferences Features From the contents expanded accordingly. The field is currently in 7 A unique collection of papers of leading Key chapters from Vol I and II (see the entries for interaction with a variety of scientific domains, specialists presenting the very recent results and each volume for the full contents lists): On Aspects including fluid dynamics, physics, electromagne- advantages in the main directions of stability of Control Theory and Instability, A. Agrachev.- tism, chemistry, biology, road and network traffic, theory in connection with fluid flows On Hamiltonian Systems,