TY - JOUR
T1 - Infinite time blow-up for the fractional heat equation with critical exponent
AU - Musso, Monica
AU - Sire, Y.
AU - Wei, Juncheng
AU - Zheng, Youquan
AU - Zhou, Yifu
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We consider positive solutions for the fractional heat equation with critical exponent {ut=-(-Δ)su+un+2sn-2sinΩ×(0,∞),u=0on(Rn\Ω)×(0,∞),u(·,0)=u0inRn,where Ω is a smooth bounded domain in Rn, n> 4 s, s∈ (0 , 1) , u: Rn× [0 , ∞) → R and u0 is a positive smooth initial datum with u0|Rn\Ω=0. We prove the existence of u0 such that the solution blows up precisely at prescribed distinct points q1, … , qk in Ω as t→ + ∞. The main ingredient of the proofs is a new inner–outer gluing scheme for the fractional parabolic problems. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
AB - We consider positive solutions for the fractional heat equation with critical exponent {ut=-(-Δ)su+un+2sn-2sinΩ×(0,∞),u=0on(Rn\Ω)×(0,∞),u(·,0)=u0inRn,where Ω is a smooth bounded domain in Rn, n> 4 s, s∈ (0 , 1) , u: Rn× [0 , ∞) → R and u0 is a positive smooth initial datum with u0|Rn\Ω=0. We prove the existence of u0 such that the solution blows up precisely at prescribed distinct points q1, … , qk in Ω as t→ + ∞. The main ingredient of the proofs is a new inner–outer gluing scheme for the fractional parabolic problems. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
U2 - 10.1007/s00208-018-1784-7
DO - 10.1007/s00208-018-1784-7
M3 - Article
SN - 0025-5831
JO - Mathematische Annalen
JF - Mathematische Annalen
ER -