【摘 要】
：
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2,ut =△u+|▽u|2u in Ω×(0, T)u = φ on (e)Ω×(0,T)u(·
【机 构】
：
UniversityofChile
【出 处】
：
非线性偏微分方程和数学物理研讨会(NPDEMP 2016)
论文部分内容阅读
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2,ut =△u+|▽u|2u in Ω×(0, T)u = φ on (e)Ω×(0,T)u(·,0)= u0 in Ω where Ω is a bounded,smooth domain in R2 and u : Ω×(0,T)→ S2,u0 :(Ω)→S2,smooth,φ= u0|(e)Ω.Given any points q1,…,qk in the domain,we find initial and boundary data so that the solution blows-up precisely at those points.
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