First, a regularity property for global solutions of some superlinear parabolic problems is established. We obtain some new a priori estimates on the global classical solutions. Applying this property to the blow-up problem, we obtain a general criterion for the occurrence of blow-up. When applied to the study of global weak solutions, we obtain some regularity results, which answers some open questions in this topic. / In this thesis, we obtain some new results on the formation of singularities for parabolic problems. We are interested in two typical singularities in parabolic evolution problems: blow-up and quenching. / Second, dichotomy properties for some porous medium equations and some semilinear parabolic equations are discussed. Some conditions on universal quenching are also obtained. When the space dimension is one, we establish a new, strong dichotomy property. Bifurcation analysis of some stationary solutions in high dimension is also investigated. / by Zheng Gaofeng. / "June 2005." / Adviser: Chou Kai-Seng. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0310. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 84-89). / 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. / Abstract in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343613 |
| Date | January 2005 |
| Contributors | Zheng, Gaofeng., 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, aperture card, microform, microfiche, 1 online resource (iv, 89 p. : ill.) |
| 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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