Irina V. Melnikova, Alexei Filinkov

Abstract Cauchy Problems (eBook, PDF)

Three Approaches

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 264
• Erscheinungstermin: 27. März 2001
• Englisch
• ISBN-13: 9781420035490
• Artikelnr.: 52972376

Autorenporträt

Melnikova, Irina V.; Filinkov, Alexei

Inhaltsangabe

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.