Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.

This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

This volume constitutes the proceedings of the Symposium on Nonlinear Evolution Equations held in Madison, October 17-19, 1977. The thirteen papers presented herein follow the order of the corresponding lectures. This symposium was sponsored by the Army Research Office, the National Science Foundation, and the Office of Naval Research.

This book presents a systematic exposition of the general theory of nonlinear contraction semigroups in Banach spaces and is aimed at students and researchers in science and engineering as well as in mathematics. Suitable for use as a textbook in graduate courses and seminars, this self-contained book is accessible to those with only a basic knowledge of functional analysis. After preprequisites presented in the first chapter, Miyadera covers the basic properties of dissipative operators and nonlinear contraction semigroups in Banach spaces. The generation of nonlinear contraction semigroups, the Komura theorem, and the Crandall-Liggett theorem are explored, and there is a treatment of the convergence of difference approximation of Cauchy problems for ????- dissipative operators and the Kobayashi generation theorem of nonlinear semigroups. Nonlinear Semigroups concludes with applications to nonlinear evolution equations and to first order quasilinear equations.

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.