Bøger i Progress in Nonlinear Differential Equations and Their Applications serien

Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc .

The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems.Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles.

A collection of articles in memory of Irene Dorfman and her research in mathematical physics. Among the topics covered are: the Hamiltonian and bi-Hamiltonian nature of continuous and discrete integrable equations; the t-function construction; and the r-matrix formulation of integrable systems.

In time, it turned out that the majority of interesting generalizations of symmetrical spaces are D'Atri spaces: natu ral reductive homogeneous spaces, Riemann manifolds whose geodesics are orbits of one-parameter subgroups, etc.

This book covers advances in linear and nonlinear aspects of the theory of partial differential equations. Includes general theory; Hardy-type inequalities; linear and non-linear hyperbolic equations; Schrodinger equations; water-wave equations and more.

Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.

Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St Petersburg Mathematical School. This book contains twenty original contributions on many topics related to V A Solonnikov's work, selected from the invited talks of an international conference held on the occasion of his 70th birthday.

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati cal Institute in the very center of St. Petersburg.

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in Joao Pessoa, Brazil, in September 2012. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations.

This book covers advances in linear and nonlinear aspects of the theory of partial differential equations. Includes general theory; Hardy-type inequalities; linear and non-linear hyperbolic equations; Schrodinger equations; water-wave equations and more.

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati cal Institute in the very center of St. Petersburg.

This volume has grown from a conference entitled Harmonic Maps, Minimal Sur­ faces and Geometric Flows which was held at the Universite de Bretagne Occi­ dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy­ namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en­ tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com­ munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit.

These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A.

This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations.

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.

This book is devoted to the sndy of some clifferentia.l inclusions motivated by Mechanics and of existcnce rcsults for the dynamics of systems with inelastic shocks, with or without friction. This ensures a certain unity of subject, techniques and applications, at the price of not including some earlier works [Mon 1-4] . In the introductory Chapter 0, sevcral essentia.l mathematical tools (either recent or recently rediscoven~d) are presented. l\1ainly they concern functions of bouncled variation defincd in real interva.ls ( deriva.tion of Stieltjcs measures, compactness results. convergencrc in tlw sense of graphs) a.ncl geometrical inequa.lities. In Chapters 1 and 2, Ivforea.u' s swecpiug process is considcred; this is a first-order differential inclusion (1) where the right-ha.nd siele is tla:' outw

Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli.

Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis;

Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. He studied singulari ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books.

This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion.

The book contains a collection of 21 original research papers which report on recent developments in various fields of nonlinear analysis. The collection covers a large variety of topics ranging from abstract fields such as algebraic topology, functional analysis, operator theory, spectral theory, analysis on manifolds, partial differential equations, boundary value problems, geometry of Banach spaces, measure theory, variational calculus, and integral equations, to more application-oriented fields like control theory, numerical analysis, mathematical physics, mathematical economy, and financial mathematics. The book is addressed to all specialists interested in nonlinear functional analysis and its applications, but also to postgraduate students who want to get in touch with this important field of modern analysis. It is dedicated to Alfonso Vignoli who has essentially contributed to the field, on the occasion of his sixtieth birthday.

Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.