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.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344414 |
| Date | January 2009 |
| Contributors | Du, Shizhong, 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, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (iv, 119 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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