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Retarded functional differential equations: a global point of view
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Mohammed, Salah Eldin A (1975) Retarded functional differential equations: a global point of view. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1747541~S15
Abstract
This work deals with some of the fundamental aspects of retarded functional differential equations (RFDE's) on a differentiable manifold. We start off by giving a solution of the Cauchy initial value problem for a RFDE on a manifold X. Conditions for the existence of global solutions are given.
Using a Riemannian structure on the manifold X, a RFDE may be pulled back into a vector field on the state space of paths on X.
This demonstrates a relationship between vector fields and RFDE's by giving a natural embedding of the RFDE's on X as a submodule of the module o* vector fields on the state space. For a given RFDE it is shown that a global solution may level out asymptotically to an equilibrium path.
Each differentiable RFDE on a Riemannian manifold linearizes in a natural way, thus generating a semi-flow on the tangent bundle to the state space. Sufficient conditions are given to smooth out the orbits and to obtain the stable bundle theorem for the semi-flow
There are examples of RFDE's on a Riemannian manifold. These include the vector fields, the differential delay equations, the delayed Cartan development and equations of Levin-Nohel type. The retarded heat equation on a compact manifold provides an example of a partial RFDE on a function space.
We conclude by making suggestions for further research.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Delay differential equations, Differentiable manifolds, Riemannian manifolds | ||||
| Official Date: | 1975 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Eells, James,1926-2007 ; Baxendale, Peter, 1948- | ||||
| Sponsors: | University of Khartoum | ||||
| Extent: | 144 leaves | ||||
| Language: | eng |
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