Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/10993
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dc.contributor.advisorBatal, Ahmet-
dc.contributor.authorYazan, Tuğba-
dc.date.accessioned2021-07-04T09:36:07Z-
dc.date.available2021-07-04T09:36:07Z-
dc.date.issued2020-07en_US
dc.identifier.citationYazan, T. (2020). Semigroup theory and some applications. Unpublished master's thesis, İzmir Institute of Technology, İzmir, Turkeyen_US
dc.identifier.urihttps://hdl.handle.net/11147/10993-
dc.descriptionThesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2020en_US
dc.descriptionIncludes bibliographical references (leaves: 53-54)en_US
dc.descriptionText in English; Abstract: Turkish and Englishen_US
dc.description.abstractn the present thesis, we consider the evolution equation (Cauchy problem) which is the basis for our study. We show how various linear partial differential equations can be transformed into the Cauchy problem form. Solving the Cauchy problem is equivalent to find a family of evolution operators T(t) which sends the initial state of the system to the solution state at a later time t. It turns out that this family of operators T(t) must satisfy some properties which we call semigroup properties. We state the Hille-Yosida and Lumer-Phillips theorems to characterize contraction semigroups. Moreover, we apply these theorems to the heat and wave equations as examples. We also consider strongly continuous operator groups and Stone's theorem. Finally, we give some essential conditions to obtain wellposed evaluation equation and introduce an inhomogeneous Cauchy problem.en_US
dc.description.abstractBu tezde, çalışmamızın temelini oluşturan ilerleme denklemi (Cauchy problemi) ele alındı. Çeşitli lineer kısmi diferansiyel denklemlerin Cauchy problem formuna nasıl dönüştürülebildiğini gösterdik. Cauchy problemini çözmek, sistemin başlangıç konumunu t zaman sonraki çözüm konumuna götüren T(t) ilerleme operatör ailesi bulmaya eşdeğerdir. Bu T(t) operatörleri ailesinin semigrup özellikleri olarak adlandırdığımız bazı özellikleri karşılaması gerektiği ortaya çıktı. Daralan semigrupları karakterize etmek için Hille-Yosida ve Lumer-Phillips teoremlerini açıkladık. Dahası bu teoremleri örnek olarak ısı ve dalga denklemlerine uyguladık. Ayrıca güçlü sürekli operatör gruplarını ve Stone teoremini de inceledik. Son olarak, iyi tanımlanmış ilerleme denklemini elde etmek ve homojen olmayan Cauchy problemini tanıtmak için bazı temel koşullar sunduk.en_US
dc.format.extentvi, 54 leavesen_US
dc.language.isoenen_US
dc.publisherIzmir Institute of Technologyen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSemigroupsen_US
dc.subjectCauchy problemen_US
dc.subjectHille-Yosida theoremen_US
dc.subjectLumer-Phillips theoremen_US
dc.titleSemigroup theory and some applicationsen_US
dc.title.alternativeSemigrup teorisi ve bazı uygulamalarıen_US
dc.typeMaster Thesisen_US
dc.authorid0000-0001-9870-3131en_US
dc.departmentThesis (Master)--İzmir Institute of Technology, Mathematicsen_US
dc.relation.publicationcategoryTezen_US
item.openairetypeMaster Thesis-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith Fulltext-
item.languageiso639-1en-
item.cerifentitytypePublications-
item.grantfulltextopen-
Appears in Collections:Master Degree / Yüksek Lisans Tezleri
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