This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

With a historical overview by Elvira Mascolo

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation. —Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. —David Jerison, MIT I usePartial Differential Equationsto prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students. —Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. —Rafe Mazzeo, Stanford University

This volume is a collection of original research papers and expository articles stemming from the scientific program of the Nonlinear PDE Emphasis Year held at Northwestern University (Evanston, IL) in March 1998. The book offers a cross-section of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. The book's contributions offer two perspectives. There are papers on general analytical treatment of the theory and papers on computational methods and applications originating from significant realistic mathematical models of natural phenomena. Also included are articles that bridge the gap between these two perspectives, seeking synergistic links between theory and modeling and computation. The volume offers direct insight into recent trends in PDEs. This volume is also available on the Web. Those who purchase the print edition can gain free access by going to www.ams.org/conm/.

This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.

This book presents a collection of selected contributions on recent results in nonlinear partial differential equations from participants to an international conference held in Fes, Morocco in 1994. The emphasis is on nonlinear elliptic boundary value problems, but there are also papers deveoted to related areas such as monotone operator theory, calculus of variations, Hamiltonian systems and periodic solutions. Some of the papers are exhaustive surveys, while others contain new results,published here for the first time. This book will be of particular interest to graduate or postgraduate students as well as to specialists in these areas.

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

These conference proceedings include papers by a number of experts with a common interest in differential equations and their application in physical and biological systems. Topics covered include direct and inverse electromagnetic scattering techniques, spatial epidemic models, wound healing, chemotaxis and reaction-diffusion equations, dynamics and stability of thin liquid films, and a contemporary formulation of symmetric linear differential equations.

The numerous applications of partial differential equations to problems in physics, mechanics, and engineering keep the subject an extremely active and vital area of research. With the number of researchers working in the field, advances-large and small-come frequently. Therefore, it is essential that mathematicians working in partial differential equations and applied mathematics keep abreast of new developments. Progress in Partial Differential Equations, presents some of the latest research in this important field. Both volumes contain the lectures and papers of top international researchers contributed at the Third European Conference on Elliptic and Parabolic Problems. In addition to the general theory of elliptic and parabolic problems, the topics covered at the conference include: applications free boundary problems fluid mechanics ogeneral evolution problems calculus of variations ohomogenization omodeling numerical analysis. The research notes in these volumes offer a valuable update on the state-of-the-art in this important field of mathematics.

This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the Collège de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.