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Title: Analysis of some deterministic and stochastic evolution equations with solutions taking values in an infinite dimensional Hilbert manifold
Author: Hussain, Javed
ISNI:       0000 0004 5368 7248
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2015
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The objective of this thesis is threefold: Firstly, to deal with the deterministic problem consisting of non-linear heat equation of gradient type. It comes out as projecting the Laplace operator with Dirichlet boundary conditions and polynomial nonlinearly of degree 2n-1, onto the tangent space of a sphere M in a Hilbert space H. We are going to deal with questions of the existence and the uniqueness of a global solution, and the invariance of manifold M i.e. if the suitable initial data lives on M then all trajectories of solutions also belong to M. Secondly, to generalize the deterministic model to its stochastic version i.e. stochastic non-linear heat equation driven by the noise of Stratonovich type. We are going to show that if the suitable initial data belongs to manifold $M$ then M-valued unique global solution to the generalized stochastic model exists. Thirdly, to investigate the small noise asymptotics of the stochastic model. A Freidlin-Wentzell large deviation principle is established for the laws of solutions of stochastic heat equation on Hilbert manifold.
Supervisor: Brzezniak, Zdzislaw Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available