An Introduction to Evolution Governed by Accretive Operators

Abstract

This chapter focuses on the evolutionary equations. The theory of partial differential equations does not have a few unifying basic results. Instead, it splits immediately into many topics, each with its own fundamental theorems and methods. However, most problems in partial differential equations arising from physical models either have the form of evolution equations, which describe the change of a physical system in time, or result from seeking stationary solutions of some evolution problem. These evolution problems can often be regarded as ordinary differential equations in some infinite–dimensional space. The chapter discusses recent results concerning abstract Cauchy problems in infinite–dimensional spaces that are close in spirit to classical ordinary differential equations. Moreover, it presents a broad range of interesting problems in partial differential equations.