Abstract/Details

THE GENERATION OF AN EVOLUTION OPERATOR IN A BANACH LATTICE

DANNON, VICTOR CHAIM. 
 University of South Florida ProQuest Dissertations Publishing,  1984. 8508845.

Abstract (summary)

Evolution equations of the type: (UNFORMATTED TABLE FOLLOWS)

(E) x' + A(t)x (CONT) f(t), t (ELEM) 0,T ,

x(0) = x(,o)

(TABLE ENDS)

are studied.

The underlying space is a general Banach lattice. The operators A(t)u are maximal lattice accretive (mL-accretive) in u and satisfy a weak smoothness condition in t. The function f(t) is an L('1)-function.

Recent results of Evans concerning general Banach spaces are extended to the present case. Namely, an evolution operator is generated for the problem (E) via a difference scheme. Functionals involving the Gateaux derivative of the norm play an important role in the development of theory.

Some applications are given in the theory of non-linear partial differential equations.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
THE GENERATION OF AN EVOLUTION OPERATOR IN A BANACH LATTICE
Author
DANNON, VICTOR CHAIM
Number of pages
71
Degree date
1984
School code
0206
Source
DAI-B 46/03, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9798662133136
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
8508845
ProQuest document ID
303325387
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303325387