Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
Preface
9
restrictionsorextensionsA|Xzforthespacesinthescale(Xz)z∈R,generated
bythisoperator.WeshowthatiftheoperatorAisclosedorsectorial
thenalltheoperatorsA|Xzarealsoclosedorsectorial.Nextwepresent
thetheoremwhichshowsthatundercertainassumptionsthescalesofthe
Banachspacescanbeachievedbyusingthemethodofcomplexinterpolation
spaces.Finallywewillgivetheexamplesthatjustifytheconsiderationof
thespaceswithfractionalexponentsonthescale.
Chapter8:dealswiththeCauchy’sproblem
{ut+Au=F(u)jt>0j
u(0)=uo.
WeconsiderthelocalXz-solutionsaswellastheirexistenceanduniqueness.
NextwerevealafewexamplesofCauchy’sproblemsforwhichwesearch
thelocalXz-solutions.
AppendixA:containsbasicfactsreferringtothetheoryofdistributions
andFouriertransform.
Acknowledgments.Iwouldliketoexpressmydeepestgratitudeto
ProfessorTomaszDłotkoforhispatience,help,thetimespentcorrecting
thisbookandtheinspirationhegavemewhenIwaswritingit.Isincerely
appreciatethecommentsonmyworkmadebythelistenersoftheSeminar
oftheDepartmentofDifferentialEquations.Iamalsogreatlyindebtedto
ProfessorPawełStrzeleckiwhosevaluableremarkssignificantlyimproved
themanuscript.Finally,IamgratefultotheInstituteofMathematicsat
theUniversityofSilesiaforthefinancialsupport.
Lastly,butaboveall,Ithankmywifeforherpatience,supportandhelp.
