### Abstract

Let Ω be a smooth bounded domain in ℝn, n ≥ 5. We consider the classical semilinear heat equation at the critical Sobolev exponent (Equation Presented) Let G(x, y) be the Dirichlet Green function of - A in Q and H(x, y) its regular part. Let qj e Q, j = 1,⋯, k, be points such that the matrix (Equation Presented) is positive definite. For any k ≥ 1 such points indeed exist. We prove the existence of a positive smooth solution u(x, t) which blows up by bubbling in infinite time near those points. More precisely, for large time t, u takes the approximate form (Equation Presented).

Original language | English |
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Pages (from-to) | 283-344 |

Number of pages | 62 |

Journal | Journal of the European Mathematical Society |

Volume | 22 |

Issue number | 1 |

Early online date | 1 Oct 2019 |

DOIs | |

Publication status | Published - 31 Jan 2020 |

### Keywords

- Critical exponent
- Green's function
- Infinite-time blow-up

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics