Finally, we get various estimates on the rupture set of the solution to the Thin Film type equations. / In the first part of the thesis, we focus on the semilinear equations with supercritical growth, and give upper bounds on the Hausdorff dimension of the singular sets for borderline solution. As a result, we can prove that the positive borderline solution must blow up in finite time. / Secondly, for the semilinear equations with critical growth, we apply a fundamental e-regularity property to illustrate the concentration phenomenon for the positive borderline solution when time goes to infinity. More precisely, we show that the lost energy can be counted exactly by the standard bubbles. / Du, Shizhong. / Adviser: Kai-Seng Chou. / Source: Dissertation Abstracts International, Volume: 70-09, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 113-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Shi-Zhong Du. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 56-58). / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- A Nondegenerate Cahn-Hilliard Type Equation --- p.11 / Chapter 2.1 --- A priori estimation --- p.13 / Chapter 2.2 --- Long time existence --- p.19 / Chapter 3 --- The Thin Film Type Equation --- p.31 / Chapter 3.1 --- Positivity for n>4 --- p.31 / Chapter 3.2 --- Improved entropy estimates --- p.36 / Chapter 4 --- Finite Speed of Propagation --- p.43 / Chapter 4.1 --- Finite speed of propagation --- p.44 / Chapter 4.2 --- The regularity of free boundary --- p.54

[Typescript] Includes bibliography.

v, 125 leaves ; 26 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1976) from the Dept. of Pure Mathematics, University of Adelaide

[Typescript] / Includes bibliography. / 170 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1967

Thesis (Ph.D. 1976) from the Department of Pure Mathematics, University of Adelaide.

Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1967. / [Typescript]. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 89-91).

by Chan Chun-hing. / Bibliography: leaves 66-68 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

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