Well-posedness questions and approximation schemes for a general class of functional differential equations
| dc.contributor.author | Turi, János | en |
| dc.contributor.committeechair | Herdman, T.L. | en |
| dc.contributor.committeemember | Burns, John A. | en |
| dc.contributor.committeemember | Wheeler, Robert L. | en |
| dc.contributor.committeemember | Cliff, Eugene M. | en |
| dc.contributor.committeemember | Beattie, C.A. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2019-02-15T21:22:05Z | en |
| dc.date.available | 2019-02-15T21:22:05Z | en |
| dc.date.issued | 1986 | en |
| dc.description.abstract | 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 R<sup>n</sup?xL<sub>p</sub>. As an example of the well-posedness of the non-atomic NFDE-system that arises in the study of aeroelasticity is established on R<sup>n</sup?xL<sub>p</sub>, 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 R<sup>n</sup?xL<sub>p</sub>, 1<p<∞, for a class of problems with atomic difference operators. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | vi, 132 leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/87661 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute and State University | en |
| dc.relation.isformatof | OCLC# 14640918 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1986.T874 | en |
| dc.subject.lcsh | Functional differential equations | en |
| dc.subject.lcsh | Banach spaces | en |
| dc.subject.lcsh | Cauchy problem | en |
| dc.title | Well-posedness questions and approximation schemes for a general class of functional differential equations | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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