Tong, Maoting
(2022)
Homogenization of the Lake Equations and the Related Topics.
PhD thesis, University of Liverpool.
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Abstract
The purpose of this thesis is to study the homogenization of the lake equation. It generates reaction effect and the reaction term is induced by homogenization due to the weak convergence. It can be characterized by L. Tartar's method of oscillating test function. We begin by the homogenization of a Stokes equation perturbed by a drift. By means of constructing a similar homogenized equation we figure out the weak limit of the important term, this leads to a limit equation with an extra zero-order term. We then turn to the homogenization of an anelastic Stokes system arising from the lake equations and prove the existence of the solution of the equation using Lax-Milgram Theorem. The homogenization of the anelastic Stokes equation lays a fundation for the homogenization of the lake equation. We finally give the proof of the existence and uniquess of the solution of lake equation using Faedo-Galerkin method and study the homogenization of the lake equation by constructing a homogenized equation of the test function according to Tartar's method.
| Item Type: | Thesis (PhD) |
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| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 22 Nov 2022 14:53 |
| Last Modified: | 18 Jan 2023 19:43 |
| DOI: | 10.17638/03166269 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3166269 |
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