Delay differential evolutions subjected to nonlocal initial conditions. (2018)

• Record Type: Book
• Further Information: Note: Monica-Dana Burlica, Mihai Necula, Daniela Rosu, Ioan I. Vrabie.
• Authors: Burlica, Monica-Dana, 1971-; Necula, Mihai; Rosu, Daniela, 1968-; Vrabie, I. I (Ioan I.), 1951-
• Contents: Preliminaries; Topologies on Banach spaces; A Lebesgue-type integral for vector-valued functions; The superposition operator; Compactness theorems; Multifunctions; C 0 -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 C 0 -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 R d ; 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 = ω; 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 (Ω); 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 (Ω) ; 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 (Ω); 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 (Ω); 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 ΓE ; Proof of Theorem 8.2.1; A reaction-diffusion system in L1 (Ω); A reaction-diffusion system in L2 (Ω); 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
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2018
• Extent: 1 online resource (362 pages)
• Subjects: 515.625; Delay differential equations; Differential equations -- Numerical solutions
• Languages: English
• ISBNs: 9781315351681; 1315351684
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