Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability — the continuous dependence of solutions on the initial conditions and the modeling equations — and on problems for which data are only prescribed on part of the boundary.