Delay differential evolutions subjected to nonlocal initial conditions

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Content: Preliminaries Topologies on Banach spaces A Lebesgue-type integral for vector-valued functions The superposition operator Compactness theorems Multifunctions C0-semigroups Mild solutions Evolutions governed by m-dissipative operators Examples of m-dissipative operators Strong solutions Nonautonomous evolution equations Delay evolution equations Integral inequalities Brezis-Browder Ordering Principle Bibliographical notes and comments Local Initial Conditions An existence result for ODEs with delay An application to abstract hyperbolic problems Local existence: The case f Lipschitz Local existence: The case f continuous Local existence: The case f compact Global existence Examples Global existence of bounded C0-solutions Three more examples Bibliographical notes and comments Nonlocal Initial Conditions: The Autonomous Case The problem to be studied The case f and g Lipschitz Proofs of the main theorems The transport equation in Rd The damped wave equation with nonlocal initial conditions The case f Lipschitz and g continuous Parabolic problems governed by the p-Laplacian Bibliographical notes and comments Nonlocal Initial Conditions: The Quasi-Autonomous Case The quasi-autonomous case with f and g Lipschitz Proofs of Theorems 4.1.1, 4.1.2 Nonlinear diffusion with nonlocal initial conditions Continuity with respect to the data The case f continuous and g Lipschitz An example involving the p-Laplacian The case f Lipschitz and g continuous The case A linear, f compact, and g nonexpansive The case f Lipschitz and compact, g continuous The damped wave equation revisited Further investigations in the case l = omega The nonlinear diffusion equation revisited Bibliographical notes and comments Almost Periodic Solutions Almost periodic functions The main results Auxiliary lemmas Proof of Theorem 5.2.1 The w-limit set The transport equation in one dimension An application to the damped wave equation Bibliographical notes and comments Evolution Systems with Nonlocal Initial Conditions Single-valued perturbed systems The main result The idea of the proof An auxiliary lemma Proof of Theorem 6.2.1 Application to a reaction-diffusion system in L2(OMEGA) Nonlocal initial conditions with linear growth The idea of the proof Auxiliary results Proof of Theorem 6.7.1 A nonlinear reaction-diffusion system in L1(OMEGA) Bibliographical notes and comments Delay Evolution Inclusions The problem to be studied The main results and the idea of the proof Proof of Theorem 7.2.1 A nonlinear parabolic differential inclusion The nonlinear diffusion in L1(OMEGA) The case when F has affine growth Proof of Theorem 7.6.1 A differential inclusion governed by the p-Laplacian A nonlinear diffusion inclusion in L1(OMEGA) Bibliographical notes and comments Multivalued Reaction-Diffusion Systems The problem to be studied The main result Idea of the proof of Theorem 8.2.1 A first auxiliary lemma The operator GAMMAE Proof of Theorem 8.2.1 A reaction-diffusion system in L1(OMEGA) A reaction-diffusion system in L2(OMEGA) Bibliographical notes and comments Viability for Nonlocal Evolution Inclusions The problem to be studied Necessary conditions for viability Sufficient conditions for viability A sufficient condition for null controllability The case of nonlocal initial conditions An approximate equation Proof of Theorem 9.5.1 A comparison result for the nonlinear diffusion Bibliographical notes and comments Bibliography Index