Nonlinear evolution equations in Banach spaces

Title page
Chapter 1 PRELIMINARIES: OPERATORS AND MILD SOLUTIONS
	1.1 Operators
	1.2 Classical and Strong Solutions
	1.3 Mild Solutions
	1.4 Mild Versus Strong
	1.5 Further Properties of Mild Solutions
	1.6 Semigroups and Generators
	1.7 Exercises
Chapter 2 ACCRETIVE 0PERATORS
	2.1 Definition and Examples of Accretive Operators
	2.2 The Bracket
	2.3 The Duality Map
	2.4 The Bracket, the Duality Map and Accretivity
	2.5 Closure and the Lim Inf
	2.6 Sums of Accretive Operators and s-accretivity
	2.7 Exercises
Chapter 3 Solutions of u' + Au \ni 0
	3.1 Existence and Uniqueness of Solutions - Statement of Results
	3.2 Solvability of General Discretizations
	3.3 The Main Estimates - Proofs
	3.4 Existence, Uniqueness and Continuity - Proofs
	3.5 Semigroups Governed by Accretive Operators
	3.6 Exercises
Chapter 4 Resolvents, the Exponential Formula and Mild Solutions of u' + Au \ni f
	4.1 The Range Condition and the Exponential Formula
	4.2 Properties of the Resolvent
	4.3 The Inhomogeneous Equation
	4.4 Exercises
Chapter 5 The Linear Case: Infinitesimal Generators and the Equation u' + Au \ni f
	5.1 Linear Terminology
	5.2 Mild Solutions of Linear Equations
	5.3 Generation of Semi groups of Bounded Linear Operators
	5.4 Variation of Parameters and the Inhomogeneous Equation
	5.5 Exercises
Chapter 6 Mild Solutions, Integral Solutions and Uniqueness
	6.1 Integral Solutions
	6.2 Integral and Mild Solutions
	6.3 Exercises
Chapter 7 Strong Solutions and Regularity of Mild Solutions
	7.1 Pointwise Derivatives of Mild Solutions
	7.2 Lipschitz Continuity and the Radon-Nikodym Property
	7.3 Differentiability of Sohitions of u' + Au \ni 0
	7.4 Refinements Under Convexity Conditions on X
	7.5 Exercises
Chapter 8 Yosida's Approximation and m-Accretive Operators
	8.1 m-Accretive Operators
	8.2 Maximal Monotone Graphs in R and Subdifferentials in Hilbert Spaces
	8.3 Properties of m-Accretive Operators and the Yosida Approximation
	8.4 Exercises
Chapter 9 m-Accretive Partial Differential Operators of first-Order
	9.1 Translation Semigroups
	9.2 The Scalar Conservation Law
		9.2.1 Comparison of Notions of Solutions of the Conservation Law
		9.2.2 A Generalized Divergence
	9.3 Hamilton-Jacobi Equations
		9.3.1 Viscosity Solutions
		9.3.2 Proofs of Propositions 9.22 and 9.23
		9.3.3 The Hamilton-Jacobi Semigroup
	9.4 Exercises
Chapter 10 m-Accretive Differential Operators of Second Order
Chapter 11 Continuous Dependence on the Data
	11.1 Convergence of Operators and Dependence on A
	11.2 An Application to Yosida Approximations
	11.3 Exercises
Chapter 12 Representation Theorems
	12.1 A Generalization of the Exponential Formula
	12.2 Product Formulas
	12.2 Exercises
Chapter 13 Solutions of u' + Au \ni f With A \in A(w)
	13.1 The Main Results
	13.2 A Reduction to the Inhomogeneous Case
	13.3 A Linear Approximation Result
	13.4 Proofs of the Main Results
	13.5 Exercises
Chapter 14 The Generalized Domain and Lipschitz Continuity of Mild Solutions
	14.1 Definition and Elementary Properties of the Generalized Domain D(A)
	14.2 D(A) and Lipschitz Continuity
	14.3 Interpretations of D(A) in X
	14.4 Exercises
Chapter 15 Advanced Existence Criteria
	15.1 A Necessary and Sufficient Condition
	15.2 Tangency Conditions
	15.3 Proof of Theorem 15.1
	15.4 Exercises
Chapter 16 Perturbation of m-accretive operators
	16.1 Relatively Continuous Perturbations
	16.2 A Characterization and Applications to Continuous Perturbations
	16.3 Perturbations in Uniformly Smooth Spaces
	16.4 A + B is Continuous in B
	16.5 Exercises
Chapter 17 Compactness
	17.1 Review of Compactness
	17.2 Compact Semigroups
	17.3 Compactness of'llajectories in the Inhomogeneous Problem
	17.4 Compactness of the Evolution Operator
	17.5 Exercises
Chapter 18 Generation of Semigroups in Special Banach Spaces
	18.1 A Summary of the Main Results
	18.2 Some Technical Le mmas
	18.3 Proofs of the Main ltesults
	18.5 Exercises
Chapter 19 Liapunov Functions, Order-Preservation and T-Accretivity
	19.1 Liapunov Functions
	19.2 Liapunov Couples and Sequences
	19.3 Convex Liapunov Functionals
	19.4 Order-Preservation and T-accretivity
	19.5 Exercises
Appendice