Abstract/Details

Zeros ofm-accretive operators and abstract evolution equations in Banach spaces

Shin, Ki-yeon. 
 University of South Florida ProQuest Dissertations Publishing,  1990. 9024915.

Abstract (summary)

In the first part of this dissertation, we approximate the solution of the equation $Tx \ni 0$ via use of differential equations associated with it. The operator $T : D(T) \subset X \to 2\sp{X}$ is at least m-accretive, where $X$ is a real Banach space.

The method of lines is used for the approximants and results of Browder are extended to general Banach spaces.

The second part of the work is devoted to the existence of solutions of perturbed abstract functional differential equation of the form:(UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\left(\eqalign{&x\sp\prime + A(t) \ni G(t, x\sb t),\cr&x(s)=\phi(s),\cr}\qquad\eqalign{&t \in \lbrack 0, T\rbrack,\cr&s\in \lbrack-r,0\rbrack,\cr}\right.$$(TABLE/EQUATION ENDS)where $A(t) : D(A(t))\subset X\to2\sp{X}$ is m-accretive and $G : \lbrack 0, T\rbrack \times C(\lbrack -r, 0\rbrack, \overline{D(A(t))})\to X$ is continuous. The dual space of $X$ is assumed to be uniformly convex and results are given under compactness or equicontinuity conditions on the evolution operator generated by $A(t)$.

Results of Pavel, Vrabie, Gutman and other authors are extended.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Zeros ofm-accretive operators and abstract evolution equations in Banach spaces
Author
Shin, Ki-yeon
Number of pages
70
Degree date
1990
School code
0206
Source
DAI-B 51/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-207-44486-4
Advisor
Kartsatos, Athanassios G.
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9024915
ProQuest document ID
303894057
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303894057