Details

Autor(en) / Beteiligte

• Chen, Guoyuan
• Wei, Juncheng
• Zhou, Yifu

Titel

Finite time blow-up for the fractional critical heat equation in Rn

Ist Teil von

• Nonlinear analysis, 2020-04, Vol.193, p.1, Article 111420

Ort / Verlag

Elmsford: Elsevier Ltd

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider the fractional critical heat equation ut+(−Δ)su=un+2sn−2s,inRn×(0,T),u(x,0)=u0(x),inRn,where 4s<n<6s, 0<s<1. For sufficiently small T>0 and given k distinct points q1,…,qk, we show that there exists an initial condition u0 such that the solution u(x,t) blows up at these k distinct points as t→T. More precisely, the blow-up profile around each concentration point takes the form of sharply scaled bubble and ‖u(⋅,t)‖L∞(Rn)∼(T−t)−n−2s6s−nas t→T.