Bücher der Reihe Progress in Nonlinear Differential Equations and Their Applications

The volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann's 70th birthday at the Banach Center in Bedlewo, Poland.

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.

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.

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.

Shape optimization problems are treated from the classical and modern perspectives. This title is suitable for graduate students in pure and applied mathematics, as well as engineers requiring a mathematical basis for the solution of practical problems.

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology).

Features research articles that are dedicated to the great French mathematician Jean Leray. This title presents a range of topics with significant results - detailed proofs - in the areas of partial differential equations, complex analysis, and mathematical physics.

Highlights developments in nonlinear analysis and differential equations. This work covers: periodic solutions of systems with p-Laplacian type operators; bifurcation in variational inequalities; a geometric approach to dynamical systems in the plane via twist theorems; and asymptotic behavior and periodic solutions for Navier-Stokes equations.

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems.

The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999).

A work that is suitbale for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. It includes a range of topics, from the treatment to results, dealing with solutions to 2D compressible Euler equations.

Phase transitions occur in several processes of physical and engineering interest. This text deals with the analysis of models of solid-liquid systems. Its main purpose is to offer an introduction to the classical Stefan problem and to some of its physically motivated extensions.

Contains the proceedings of the international workshop Variational Problems in Materials Science. This book talks about the study of variational problems in materials science, how it has contributed a lot in shaping our understanding on how materials work and perform. It also talks about analytical techniques and of physical systems and phenomena.

This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets.

Covers the advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. This work features chapters on computational aspects and applications to biology. It is suitable for researchers and graduate students.

Contains research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. This work considers topics of nonlinear analysis, such as calculus of variations, variational inequalities, critical point theory, equations of Hamilton-Jacobi, Schrodinger and Navier-Stokes, and free boundary problems.

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

Harmonic maps are solutions to a natural geometrical variational prob lem. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science.

Devoted to minimax theorems and their applications to partial differential equations, this text presents these theorems in a simple and unified way, starting from a quantitative deformation lemma. Many applications are given to problems dealing with lack of compactness.

In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features.

Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

This volume presents lectures from the Danish-Swedish Analysis Seminar 1995, covering themes in mathematical physics, spanning a wide variety of topics.

The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research.

A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples.

The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987.