عنوان

Semigrup teorisi ve bazı uygulamaları

Number

TLpq2522830464

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Semigrup teorisi ve bazı uygulamaları

General Material Designation

[Thesis]

First Statement of Responsibility

Yazan, Tuğba

Subsequent Statement of Responsibility

Batal, Ahmet

Name of Publisher, Distributor, etc.

Izmir Institute of Technology (Turkey)

Date of Publication, Distribution, etc.

2020

Specific Material Designation and Extent of Item

61

Dissertation or thesis details and type of degree

Master's

Body granting the degree

Izmir Institute of Technology (Turkey)

Text preceding or following the note

2020

Text of Note

In 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.

Cauchy problems

Mathematical functions

Mathematics

Batal, Ahmet

Yazan, Tuğba

Electronic name

p

[Thesis]

276903

a

Y