Convergence to steady state for a phase field system with memory [Elektronische Ressource] / Vicente Vergara

CONVERGENCE TO STEADY STATE FOR A PHASEFIELD SYSTEM WITH MEMORYDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)vorgelegt derMathematisch-Naturwissenschaftlich-Technischen Fakultat¨(mathematisch-naturwissenschaftlicher Bereich)der Martin-Luther-Universitat Halle-Wittenberg¨vonHerrn M.Sc. Vicente Vergarageb. am: 05. Januar 1973 in: Santiago (Chile)Gutachter:Prof. Dr. Jan Pruss, Halle (Saale)¨Prof. Dr. Philippe Cl´ement,DelftHalle (Saale), 13.06.2006 (Tag der Verteidigung)urn:nbn:de:gbv:3-000010416[http://nbn-resolving.de/urn/resolver.pl?urn=nbn%3Ade%3Agbv%3A3-000010416]Table of ContentsTable of Contents iAcknowledgements iiiIntroduction 11 Mathematical Preliminaries 111.1 Sectorialoperators.................................. 121.1.1 Examples................................... 161.2 Operator-valuedFourierMultipliers ....................... 181.3 Sumsofclosedlinearoperators.......................... 191.4 AbstractparabolicVolteraequations ...................... 201.4.1 Resolvent families .............................. 201.4.2 Maximal regularity in L 21p2 Physical background 252.1 Heat conduction ................................... 252.2 Phasefieldsystemswithmemory......................... 272.2.1 Conservedmodel 273 A non-conserved phase field model 313.1 Localwell-posedness ................................ 313.1.1 Contractionmappingprinciple ...................... 373.