Nonlinear Evolutions

Ki Sik Ha
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Ki Sik Ha: Pusan National University, Department of Mathematics

Chapter Chapter 1 in Nonlinear Functional Evolutions in Banach Spaces, 2003, pp 1-30 from Springer

Abstract: Abstract The purpose of this chapter is to state some basic concepts and to introduce well known results in the nonlinear operator theory and the theory of nonlinear evolutions in real Banach spaces that will play very important roles in the subsequent development of this book. In Section 1.1 we consider properties of accretive operators with one-sided directional derivatives and duality mappings. Section 1.2 contains the generation of nonlinear semigroups and solutions of autonomous homogeneous nonlinear evolutions. Section 1.3 deals with the existence for strong solutions, integral solutions, and limit solutions of autonomous non-homogeneous nonlinear evolutions. Section 1.4 is devoted to definitions and properties of generalized domains. Section 1.5 treats properties of evolution operators and their generation. In Section 1.6, Section 1.7, and Section 1.8 we discuss how to solve non-autonomous nonlinear evolutions by Crandall-Liggett, Crandall-Pazy, and Evans, respectively, whilst Section 1.9 deals with them by Pavel’s method. Comments and notes for references are found in Section 1.10.

Keywords: Strong Solution; Evolution Operator; Nonlinear Evolution; Generalize Domain; Integral Solution (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-94-017-0365-9_1

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