Abstract/Details

Nonlinear inclusions of elliptic type and methods of lines for evolution problems in Banach spaces

Liu, Xiaoping. 
 University of South Florida ProQuest Dissertations Publishing,  1994. 9504490.

Abstract (summary)

The first part of this work concerns itself with the study of inclusions$$Tx + Cx\ni p,\eqno(*)$$where $T: X \supset D(T)\to 2\sp{X}$ is usually a (possibly nonlinear) m-accretive operator and $C: \overline{D(T)}\to X$ is usually a (possibly nonlinear) compact operator in a Banach space X. Several new results are given for (*) which involve applications of the Leray-Schauder Degree Theory. In particular, considerable improvements have been made possible of recent results of Zhu for (*) and Yang for a triplet of operators. The second part of this work involves the construction and the proof of the convergence of a method of lines for the quasi-nonlinear problem:$$\eqalign{&x\sp\prime + A(t,x\sb{t})x\ni G(t,x\sb{t}, L\sb{t}x), t\in\lbrack 0, T\rbrack,\cr&x\sb0 = \phi,}$$where the operators $A(t,\psi)$: $X\supset D(A(t,\psi))\to 2\sp{X}$ are at least m-accretive and the operators $G(t,\psi\sb1,\psi\sb2)$ are Lipschitzian. This method is more general and considerably more direct than the method developed by Ha, Shin and Jin.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; evolution equations
Title
Nonlinear inclusions of elliptic type and methods of lines for evolution problems in Banach spaces
Author
Liu, Xiaoping
Number of pages
97
Degree date
1994
School code
0206
Source
DAI-B 55/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-209-32837-7
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
9504490
ProQuest document ID
304170897
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304170897