Work

Blow-up of the critical norm for a supercritical semilinear heat equation

Year: 2024

Type: article

Abstract: We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation u_{t}=\Delta u+|u|^{p-1}u in an arbitrary C^{2+\alpha} domain of \mathbf{R}^{n} . In the range p>p_{S}:=(n+2)/(n-2) , we show that the critical norm must be unbounded near the blow-up time, where the type I blow-up condition is not imposed. The range p>p_{S} is optimal in view of the existence of type II blow-up solutions with bounded critical norm for p=p_{S} .

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1551

Authors: Hideyuki Miura, Jin Takahashi

Institution: Institute of Science Tokyo

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W4403378315

FWCI: 0.764

Cites:

Cited by: 1

Related to: 10