Alexei Filinkov & Irina V. Melnikova 
Abstract Cauchy Problems [PDF ebook] 
Three Approaches

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