Bøger i Progress in Nonlinear Differential Equations and Their Applications serien

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.

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).

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).

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis. The text discusses key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, and more.

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.

Collects contributions by specialists in the domain of elliptic partial differential equations and geometric flows. This work is useful for students and researchers in the fields of elliptic and parabolic partial differential equations that arise from variational problems, as well as researchers in fields such as particle physics and optimization.

The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 k n-1. The core of the book discusses the case k = n, and then the case 1 k n-1 with special attention on the case k = 2, which is fundamental in symplectic geometry.

Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.

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.

In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points.

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

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.

This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension.

A collection of 31 research papers that reflects the author's interest and influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces.

In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads.

Consists of 14 research articles that are an outgrowth of a scientific meeting held in Cortona on the subject of Carleman Estimates and Control Theory. This volume includes topics such as unique continuation for elliptic PDEs and systems, control theory and inverse problems. It is suitable for researchers and graduate students of pdes.

This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. Still other work was published in standard books or journals, but written in Russian or French.

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.