Date | Mar 20, 2024 |
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Speaker | Hideyuki Miura |

Dept. | Tokyo institute of technology |

Room | 27-116 |

Time | 15:00-16:30 |

We consider the critical norm blow-up problem for the nonlinear heat equation with power type nonlinearity |u|^{p-1}u in R^n.

In the Sobolev supercritical range p>(n+2)/(n−2), we show that if the maximal existence time T is finite, the scaling critical L^q norm of the solution becomes infinite at t=T. The range of p is optimal in view of known examples of blow-up solutions with the bounded critical norm for the Sobolev critical case. This is a joint work with Jin Takahashi (Tokyo institute of technology).

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