Filling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions.
After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial conditions, examine delay evolution inclusions, and extend some results to the multivalued case of reaction-diffusion systems. The book concludes with results on viability for nonlocal evolution inclusions.
Table of Contents:
Preliminaries. Local Initial Conditions. Nonlocal Initial Conditions: The Autonomous Case. Nonlocal Initial Conditions: The Quasi-Autonomous Case. Almost Periodic Solutions. Evolution Systems with Nonlocal Initial Conditions. Delay Evolution Inclusions. Multivalued Reaction-Diffusion Systems. Viability for Nonlocal Evolution Inclusions. Bibliography. Index.
About the Author :
Monica-Dana Burlică is an associate professor in the Department of Mathematics and Informatics at the “G. Asachi” Technical University of Iaşi. She received her doctorate in mathematics from the University “Al. I. Cuza” of Iaşi. Her research interests include differential inclusions, reaction-diffusion systems, viability theory, and nonlocal delay evolution equations.
Mihai Necula is an associate professor in the Faculty of Mathematics at the University "Al. I. Cuza” of Iaşi. He received his doctorate in mathematics from the University “Al. I. Cuza” of Iaşi. His research interests include differential inclusions, viability theory, and nonlocal delay evolution equations.
Daniela Roşu is an associate professor in the Department of Mathematics and Informatics at the “G. Asachi” Technical University of Iaşi. She received her doctorate in mathematics from the University "Al. I. Cuza” of Iaşi. Her research interests include evolution equations, viability theory, and nonlocal delay evolution equations.
Ioan I. Vrabie is a full professor in the Faculty of Mathematics at the University "Al. I. Cuza” of Iaşi and a part-time senior researcher at the "O. Mayer" Mathematical Institute of the Romanian Academy. He received his doctorate in mathematics from the University “Al. I. Cuza” of Iaşi. He has been a recipient of several honors, including The First Prize of the Balkan Mathematical Union and the “G. Ţiţeica” Prize of the Romanian Academy. His research interests include evolution equations, viability theory, and nonlocal delay evolution equations.
Review :
"This book will be useful to researchers and graduate students interested in delay evolution equations and inclusions subjected to nonlocal initial conditions." - Sotiris K. Ntouyas (Ioannina)
