Green's function and infinite-time bubbling in the critical nonlinear heat equation

  • Carmen Cortázar

    Pontificia Universidad Católica de Chile, Santiago, Chile
  • Manuel del Pino

    University of Bath, UK and Universidad de Chile, Santiago, Chile
  • Monica Musso

    University of Bath, UK and Pontificia Universidad Católica de Chile, Santiago, Chile
Green's function and infinite-time bubbling in the critical nonlinear heat equation cover

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Abstract

Let be a smooth bounded domain in , . We consider the classical semilinear heat equation at the critical Sobolev exponent

Let be the Dirichlet Green's function of in and its regular part. Let , , be points such that the matrix

is positive definite. For any such points indeed exist. We prove the existence of a positive smooth solution which blows-up by bubbling in infinite time near those points. More precisely, for large time , takes the approximate form

Here and , as . We find that as .

Cite this article

Carmen Cortázar, Manuel del Pino, Monica Musso, Green's function and infinite-time bubbling in the critical nonlinear heat equation. J. Eur. Math. Soc. 22 (2020), no. 1, pp. 283–344

DOI 10.4171/JEMS/922