Existence and flow invariance of solutions to non-autonomous partial differential delay equations [Elektronische Ressource] / vorgelegt von Seyedeh Marzieh Ghavidel

Existence and Flow Invariance of Solutions toNon-autonomous Partial Differential DelayEquationsDem FachbereichMathematikder Universit¨at Duisburg-Essenzur Erlangung desDoktorgrades (Dr. rer. nat.)vorgelegt vonSeyedeh Marzieh Ghavidelaus dem IranNovember 2007Vorsitzender: Prof. Dr. Jur¨ gen HerzogErster Gutachter: Prof. Dr. Wolfgang M. RuessZweiter Gutachter: Prof. Dr. Dieter BotheDedicated to my husband and my son AliAcknowledgmentsI am very grateful to my advisor Professor Wolfgang Ruess for his guidance,constant encouragement and support throughout the preparation of this thesis.IalsoexpressmygratitudetotheuniversityofDuisburg–Essenforitshospitalityand the facilities provided during my Ph.D study and research.Finally, I would like to thank the ministry of science, research and technology ofthe Islamic Republic of Iran for the financial support offered to me during my study.ContentsPreface 11 Preliminaries 51.1 Accretive operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Non–autonomous Cauchy problems . . . . . . . . . . . . . . . . . . . 71.3 Evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Existence and flow-invariance under local range conditions 112.1 The initial history space . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Existence of mild solutions to (FDE) . . . . . . . . . . . . . . . . . .