Abstract Cauchy Problems

ISBN-13: 9780367397470 / Angielski / Miękka / 2019 / 264 str.

Irina V. Melnikova; Alexei Filinkov

Opis

Relevant to a variety of mathematical models in physics, engineering, and finance, this volume studies Cauchy problems that are not well-posed in the classical sense. It brings together and examines three major approaches to treating such problems: semigroup methods, abstract distribution methods, and regularization methods. Although extensively developed over the last decade, the authors provide a unique, self-contained account of these methods and demonstrate the profound connections between them. Accessible to beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.

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