Friday, February 19, 2016 - 15:30 to 16:30
704 Thackeray
Abstract or Additional Information
We consider the harmonic map flow from a bounded two-dimensional domain to S2: u:Ω→S2, ut=Δu+|∇u|2u. Here we don't assume any symmetry on the domain. We construct Type II blow up solutions and prove that the blow rate (T−t)/log2(T−t) is universal and stable in general domains. We also construct multiple and reverse bubblings. As a consequence we can perform a new geometric surgery for continuation of solutions after bubbling. If time permits, other Type II blow up problems, such as Keller-Segel and critical exponent problems will be discussed as well. (Joint work with Manuel del Pino and Juan Davila.)
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HOST: Huiqiang Jiang