- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- On non-linear time-lag evolution equations
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
On non-linear time-lag evolution equations Lam, Che-Bor
Abstract
The purpose of this thesis is to obtain existence theorems for perturbated evolution equations in Hilbert spaces and Banach spaces. A practical example of the perturbations under consideration is an operator with a time-lag or delayed argument. Throughout the thesis, the Galerkin approximation method will be used to establish the existence theorems. In chapter one, we study the problem in Hilbert spaces. The key is to obtain a priori estimates on the time fractional derivatives of the approximate solutions. We shall prove that there exists a solution with time fractional derivatives of order less than 1/2. In chapter two, we consider the problem in Banach spaces. Again, we apply the Galerkin approximation method, but with a special basis. In chapter three, we study periodic solutions of evolution equations. Here we use the Schauder-Tychonov fixed point theorem to prove the existence of periodic solution to the approximating equations. In the last chapter, we give examples of appliactions of the various theorems proved in the first three chapters.
Item Metadata
Title |
On non-linear time-lag evolution equations
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1972
|
Description |
The purpose of this thesis is to obtain existence theorems for perturbated evolution equations in Hilbert spaces and Banach spaces. A practical example of the perturbations under consideration is an operator with a time-lag or delayed argument. Throughout the thesis, the Galerkin approximation method will be used to establish the existence theorems.
In chapter one, we study the problem in Hilbert spaces. The key is to obtain a priori estimates on the
time fractional derivatives of the approximate solutions. We shall prove that there exists a solution with time fractional derivatives of order less than 1/2. In chapter two, we consider the problem in Banach spaces. Again, we apply the Galerkin approximation method, but with a special basis. In chapter three, we study periodic solutions of evolution equations. Here we use the Schauder-Tychonov fixed point theorem to prove the existence of periodic solution to the approximating equations. In the last chapter, we give examples of appliactions of the various theorems proved in the first three chapters.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2011-03-04
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0080469
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.