Semilinear Cauchy Problems with Non-dense Domain

Abstract

The main purpose of this chapter is to present a comprehensive semilinear theory that will allow us to study the properties of solutions of the non-densely defined Cauchy problems, such as existence and uniqueness of a maximal semiflow, positivity, Lipschitz perturbation, differentiability with respect to the state variable, time differentiability, classical solutions, stability of equilibria, etc.