Abstract Cauchy Problems: Three Approaches

ISBN-13: 9781584882503 / Angielski / Twarda / 2001 / 264 str.

A. I. Filinkov; I. V. Mel'nikova; Irina V. Melnikova

Opis

This Research Note addresses several pivotal problems in spectral theo ry and nonlinear functional analysis in connection with the analysis o f the structure set of zeroes of a general class of nonlinear operator s. Appealing to a broad audience, it contains many important contribut ions to linear algebra, linear functional analysis, nonlinear function analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and system. The result s presented cover a thirty-year period and cut across a variety of mat hematical fields.

Spis treści

Preface. Introduction. ILLUSTRATION AND MOTIVATION. Heat Equation. The Reversed Cauchy Problem for the Heat Equation. Wave Equation. SEMIGROUP METHODS. C0-Semigroups. Integrated Semigroups. k-Convoluted Semigroups. C-Regularized Semigroups. Degenerate Semigroups. The Cauchy Problem for Inclusions. Second Order Equations. ABSTRACT DISTRIBUTION METHODS. The Cauchy Problem. The Degenerate Cauchy Problem. Ultradistributions and New Distributions. REGULARIZATION METHODS. The Ill-Posed Cauchy Problem. Regularization and C-Regularized Semigroups. BIBLIOGRAPY. GLOSSARY OF NOTATION. INDEX.

O autorze

Melnikova, Irina V.; Filinkov, Alexei