The stochastic nonlinear heat equation

Carroll, Andrew

Abstract

This thesis considers a stochastic partial differential equation which may be viewed as a stochastic version of the nonlinear heat equation studied by Eells and Sampson. The special case of loops on a compact Riemannian manifold M is studied, where the loop is parametrised by the unit circle. Using ideas of Eells and Sampson and the theory of stochastic evolution equations on infinite dimensional M-type 2 Banach spaces, existence and uniqueness of an M-valued solution is shown, where M is a certain Sobolev-Slobodetski space of loops on the manifold M. In particular M is an infinite
dimensional manifold modelled on an M-type 2 Banach space.

Finally, an approximation result of the Wong-Zakai type for Stratonovich integrals in M-type 2 Banach spaces is given.

Citation

Carroll, A. The stochastic nonlinear heat equation. (Thesis). University of Hull. https://hull-repository.worktribe.com/output/4227203

• Thesis Type: Thesis
• Deposit Date: Jul 3, 2018
• Publicly Available Date: Mar 2, 2023
• Keywords: Mathematics
• Public URL: https://hull-repository.worktribe.com/output/4227203
• Additional Information: Department of Mathematics, The University of Hull
• Award Date: May 1, 1999