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We consider the Cauchy problem for the energy critical heat equation ut = ∆u + u3 in R4 × (0, T), (1) (u(·, 0) = u0 in R4. 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 (1) blows up at exactly those k points with a type II rate, namely larger than (T − t)− 2 . In 1 fact ku(·, t)k∞ ∼ (T − t)− 1 log2(T − t). The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin-Talenti bubbles.
|Number of pages||9|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 30 Jun 2020|
- Construction of blow-up solution
- Energy critical heat equation
- Inner–outer gluing method
- Type II finite time blow-up
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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- 1 Active
27/04/20 → 31/03/24
Project: Research council