Preliminaries

Abstract

The aim of this Chapter is to provide some basic results that we will use frequently in the chapters that follow. Most results presented here are given without proof. We refer the reader to the appropriate monographs or textbooks where details can be found.

Keywords: real functions, functions of bounded variation, integral formulas, abstract approximation theory, nonlinear functional analysis, distributions, operator theory, semigroups of nonlinear operators, optimal control, numerical analysis, finite difference methods, finite element method, nonlinear systems, fractional steps method, phase changes, mathematical modeling, applications in industry.