Semigroups of Linear and Nonlinear Operations and Applications

This is the first publication which follows an agreement by Kluwer Publishers with the Caribbean Mathematics Foundation (CMF), to publish the proceedings of its mathematical activities. To which one should add a disclaimer of sorts, namely that this volume is not the first in a series, because it is not first, and be cause neither party to the agreement construes these publications as elements of a series. Like the work of CMF, the arrangement between it and Kluwer Publishers, evolved gradually, empirically. CMF was created in 1988, and inaugurated with a conference on Ordered Algebraic Structures. Every year since there have been gatherings on a variety of mathematical topics: Locales and Topological Groups in 1989; Positive Operators in 1990; Finite Geometry and Abelian Groups in 1991; Semigroups of Operators last year. It should be stressed, however that in preparing for the first conference, there was no plan which might have augured what came after. One could say that one thing led to another, and one would be right enough.

Klappentext

This book provides a useful review of the current state of the art in semigroups of linear and nonlinear operators and applications. In addition to short introductory course notes in the linear and nonlinear theories, many of the leading researchers in the field contributed articles which are notable for their expository emphasis. Application areas include reaction-diffusion systems, other parabolic problems, scattering theory, fluid dynamics, continuum mechanics, mathematical biology. There is much emphasis on existence results, regularity properties, asymptotics, and problems that are not well-posed in the usual sense. For graduate students and researchers interested in the applications of operator theory and functional analysis to differential equations. Researchers in mathematical physics and mathematical biology and control theory will profit from the expository account of recent developments in semigroup theory motivated by the applications.

Inhalt
A Survey of Semigroups of Linear Operators and Applications.- Nonlinear Semigroups and Applications.- A Bifucation Problem for Point Interactions in L1(IR3).- Semipositone Problems.- A Generation Result for C-regularized Semigroups.- Smoothing Properties of Heat Semigroups in Infinite Dimensions.- Locally Stable Dynamics for Reaction-Diffusion Systems.- Global Dynamics of Singularly Perturbed Hodgkin-Huxley Equations.- On Strongly Elliptic Differential Operators on L1(IRn).- Stability and Local Invariant Manifolds in Fully Nonlinear Parabolic Equations.- Fractional Integrals and Semigroups.- Spectral and Asymptotic Properties of Strongly Continuous Semigroups.- Continuation for Quasiholomorphic Semigroups.- Global Existence for a Reaction-Diffusion System with a Balance Law.- Convexity of the Growth Bound of C0-semigroups of Operators.