科研之友
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摘要
We consider the Cauchy problem for the energy critical heat equation ■ in dimension n = 5. More precisely we find that for given points q1, q2,..., qk and any sufficiently small T > 0 there is an initial condition u0 such that the solution u(x, t) of(0.1) blows-up at exactly those k points with rates type Ⅱ, namely with absolute size ～(T-t)-α for α >3/4. The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin–Talenti bubbles.
