Dynamics of Evolutionary Equations Book

	Preface
Ch. 1	The Evolution of Evolutionary Equations	1
Ch. 2	Dynamical Systems: Basic Theory	11
2.1	Semiflows and Nonlinear Semigroups	12
2.2	Compact and [kappa]-Contracting Semiflows	22
2.3	Attractors and Global Attractors	27
2.4	Skew Product Dynamics and Nonautonomous Equations	45
2.5	Singular Semiflows	48
Ch. 3	Linear Semigroups	61
3.1	C[subscript 0]-Semigroups and Infinitesimal Generators	62
3.2	An Illustrative Example	66
3.3	Compact and [kappa]-Contracting C[subscript 0]-Semigroups	69
3.4	Hille-Yosida and Lumer-Phillips Theorems	69
3.5	Differentiable Semigroups	73
3.6	Analytic Semigroups and Sectorial Operators	76
3.7	Fractional Powers and Interpolation Spaces	92
3.8	Illustrations	103
3.9	Perturbation Theory	126
Ch. 4	Basic Theory of Evolutionary Equations	141
4.1	PDEs as Evolutionary Equations	143
4.2	Solution Concepts and the Variation of Constants Formula	146
4.3	Linear Skew Product Semiflows	172
4.4	Perturbations of Analytic Semigroups	175
4.5	Exponential Dichotomies: Existence and Robustness	190
4.6	Well-Posed Problems: C[subscript 0]-Theory	224
4.7	Well-Posed Problems: Analytic Theory	232
4.8	Regularity and Compactness Properties	244
4.9	The Linearized Equation	247
Ch. 5	Nonlinear Partial Differential Equations	267
5.1	Reaction Diffusion Equations	269
5.2	Nonlinear Wave Equations	284
5.3	Equations of Convection	313
5.4	Kuramoto-Sivashinsky Equation	319
5.5	Cahn-Hilliard Equation	328
Ch. 6	Navier-Stokes Dynamics	359
6.1	Formulation as a Nonlinear Evolutionary Equation	361
6.2	Bubnov-Galerkin Approximations	369
6.3	Weak Solutions	373
6.4	Strong Solutions	396
6.5	Navier-Stokes Dynamics: Global Attractors	416
6.6	The Kwak Transformation	426
6.7	Related Nonlinear Systems	430
6.8	Proofs for the Bubnov-Galerkin Approximations	436
Ch. 7	Major Features of Dynamical Systems	457
7.1	Local Dynamics Near an Equilibrium	460
7.2	Dynamics of Gradient Systems	483
7.3	Behavior Near a Periodic Orbit	488
7.4	Invariant Manifolds	490
7.5	Applications	541
7.6	Nonautonomous Problems	553
7.7	Other Topics of Dynamical Systems	553
Ch. 8	Inertial Manifolds: The Reduction Principle	569
8.1	Introduction	570
8.2	The Lyapunov-Perron Method	575
8.3	Existence of Inertial Manifolds: Spectral Gap Condition	577
8.4	Exponential Attraction of Inertial Manifolds	582
8.5	Smoothness of Inertial Manifolds	585
8.6	Applications of Inertial Manifold Theorems	589
8.7	Open Problems for Inertial Manifolds	591
App	Basics of Functional Analysis	593
	Bibliography	629
	Notation Index	655
	Subject Index	659