nonlinear evolution equations

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1、SONGMUZHENGNONLINEAREVOLUTIONEQUATIONSCRCPRESSBocaRatonLondonNewYorkWashington,D.C.ContentsPreface...........................................................xi1.Preliminaries....................................................11.1.MotivationsfromOtherBranchesofScience........

2、......11.2.LocalSolutionsandGlobalSolutions.....................41.3.SomeBasicKnowledgeonSobolevSpacesandPDE......81.3.1SobolevSpacesWm;p(Ω)...........................81.3.2TheGagliardo–NirenbergandPoincar´eInequalities101.3.3AbstractFunctionsValuedinBanachSpaces......111.3.4

3、LinearEllipticBoundaryValueProblems..........121.3.5InterpolationSpaces...............................151.3.6NotationandSomeUsefulInequalities............171.4.BibliographicComments................................192.SemigroupMethod............................................

4、.212.1.SemigroupsofLinearContractionOperators............212.1.1Semigroups.......................................212.1.2TheInfinitesimalGenerator.......................232.2.Hille-YosidaTheorem...................................262.3.RegularitiesofSolutions....................

5、............352.4.Non-homogeneousEquations............................412.5.SemilinearEquations....................................462.6.AnalyticSemigroups....................................592.7.Applications............................................702.8.BibliographicComm

6、ents................................933.CompactnessMethodandMonotoneOperatorMethod.........953.1.CompactnessMethod...................................953.1.1.SomeResultsonConvergenceandCompactness..96viiviiiContents3.1.2.MethodandExamples..........................1043.2.Monoto

7、neOperatorMethod...........................1143.2.1.GeneralFramework.............................1153.2.2.Applications....................................1253.2.3.GeneralizationsandSupplements................1283.3.BibliographicComments...............................1304.Mono

8、toneIterativeMethodandInvariantRegions.............1334.1.Introducti