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：Type Ⅱ Blow-up in the 5-dimensional Energy Critical Heat Equation论文

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作者（2019）在《Type Ⅱ Blow-up in the 5-dimensional Energy Critical Heat Equation》一文中研究指出：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.

Abstract

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.

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