Abstract Cauchy Problems: Three Approaches (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in numerous mathematical models in physics, engineering, and finance can be approached in a variety of ways.The authors structured these approaches, identifying three main strategies for dealing with ill-posed problems: semigroup methods, abstract distribution methods, and regularization methods.Semigroup and distribution methods restore well-posedness, in a modern weak sense.Regularization methods provide approximate solutions to ill-posed problems.Although these approaches have been extensively developed by many researchers, a comprehensive treatment of all three approaches has hitherto been unforthcoming. Abstract Cauchy Problems: Three Approaches, now in its second edition, provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them.The authors discuss the application of different methods