Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.465962
Title: Retarded functional differential equations : a global point of view
Author: Mohammed, Salah Eldin A.
ISNI:       0000 0001 1781 448X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1975
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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.
Supervisor: Not available Sponsor: University of Khartoum
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.465962  DOI: Not available
Keywords: QA Mathematics
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