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Type of Document Dissertation Author Wang, Shuangcai Author's Email Address swang1@nd.edu URN etd-12082006-212708 Title Blowup in Nonliear Heat Equations Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Grant J. Mathews Committee Chair Bei Hu Committee Member Gerard K. Misiolek Committee Member Israel Michael Sigal Committee Member Mark S. Alber Committee Member Keywords
- partial differential equations
- blowup
Date of Defense 2006-09-08 Availability unrestricted Abstract We study the blowup problem for nonlinear heat equations. We show that if the even initial value is close enough to a 2-dimensional manifold of approximately homogenous solutions, the solution blows up in a finite time and the asymptotical profile is an approximate solution with parameters evolving according to a certain dynamical system plus a small fluctuation in $L^infty$.
The result allows us to construct initial data with more than one local maximum while the solutions still blow up in a finite time according to the asymptotical profile. We also demonstrated that there is an open subset in the space of initial data and their solutions blow up according to the described asymptotical profile.
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