ZelenyaK在一九六八年證明了所有二階擬線性拋物方程的有界全域解都會趨向一個穩態解，而其證明中的一個重要部分就是證明所有這類方程都存在一個數土結構，這是高階方程不定會有的。在這篇論文中，我們會證明Zelenyak 定理，以及找出一個四階、六階方程存在變分結構的充分必要條件。 / Zelenyak proved in 1968 that every bounded global solution of a second order quasilinear parabolic equation converges to a stationary solution. An important part in the proof is that every such equation has a variational structure. For higher order parabolic equations, this is not the case. In this thesis, we prove Zelenyak's theorem and find a necessary and sufficient condition for a fourth or sixth order equation to be variational. / Detailed summary in vernacular field only. / Chan, Hon To Hardy. / "October 2012." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leave 66). / Abstracts also in Chinese. / Introduction --- p.1 / Chapter 1 --- Convergence of Global Solutions of Second Order Parabolic Equations --- p.5 / Chapter 1.1 --- Main result --- p.5 / Chapter 1.2 --- Four auxiliary lemmas --- p.6 / Chapter 1.3 --- Proof of main result --- p.15 / Chapter 1.4 --- An extension to fourth order equations --- p.21 / Chapter 1.4.1 --- An example --- p.25 / Chapter 2 --- The Multiplier Problem for the Fourth Order Equa-tion --- p.28 / Chapter 2.1 --- Introduction --- p.28 / Chapter 2.2 --- Main results --- p.31 / Chapter 2.2.1 --- A necessary and sufficient condition for a variational structure --- p.31 / Chapter 2.2.2 --- An algorithm to check the existence of a variational structure --- p.32 / Chapter 2.3 --- Proof of main results --- p.33 / Chapter 2.4 --- Examples --- p.48 / Chapter 3 --- The Multiplier Problem for the Sixth Order Equa-tion --- p.52 / Chapter 3.1 --- Introduction --- p.52 / Chapter 3.2 --- Main results --- p.55 / Chapter 3.2.1 --- A necessary and sufficient condition for a variational structure --- p.55 / Chapter 3.2.2 --- An algorithm to check the existence of a variational structure --- p.56 / Chapter 3.3 --- Proof of main results --- p.59 / Bibliography --- p.66
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328612 |
| Date | January 2013 |
| Contributors | Chan, Hon To Hardy., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (5, 66 leaves) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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