Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat

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.