Well-posedness questions and approximation schemes for a general class of functional differential equations

In this paper we consider approximation schemes and questions of well-posedness for a general class of functional differential equations of neutral-type (NFDE) where the difference operator does not have an atom at zero. Equations of this type occur in the modeling of certain aeroelastic control problems and include many singular integro-differential equations. We obtain general necessary and sufficient conditions for the well-posedness of functional differential equations of neutral-type on the Banach-spaces RⁿxL_p. As an example of the well-posedness of the non-atomic NFDE-system that arises in the study of aeroelasticity is established on RⁿxL_p, 1≤p<2. Employing the equivalence between generalized solutions of NFDEs and mild solutions of the “corresponding” abstract Cauchy-problems, we make use of general approximation results for well-posed Cauchy-problems to establish and analyze the convergence of the “averaging projection” scheme on the Banach spaces RⁿxL_p, 1<p<∞, for a class of problems with atomic difference operators.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1986

Author dc:creator

• Turi, János

Chair dc:contributor.committeechair

• Herdman, T.L.

Committee members dc:contributor.committeemember

• Burns, John A.
• Wheeler, Robert
• Cliff, Eugene M.
• Beattie, Christopher A.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/87661

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/87661