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. 283–344DOI 10.4171/JEMS/922