TY - JOUR
T1 - No local L1 solutions for semilinear fractional heat equations
AU - Li, Kexue
N1 - Publisher Copyright:
© 2017 Diogenes Co., Sofia 2017.
PY - 2017/12/20
Y1 - 2017/12/20
N2 - We study the Cauchy problem for the semilinear fractional heat equation ut = Δα/2 u + f(u) with non-negative initial value u0 ϵ Lq(ℝn) and locally Lipschitz, non-decreasing, non-negative source term f. For f satisfying the Osgood-type condition f1∞dsf(s)=∞, we show that there exist initial conditions such that the equation has no local solution in Lloc1(Rn).
AB - We study the Cauchy problem for the semilinear fractional heat equation ut = Δα/2 u + f(u) with non-negative initial value u0 ϵ Lq(ℝn) and locally Lipschitz, non-decreasing, non-negative source term f. For f satisfying the Osgood-type condition f1∞dsf(s)=∞, we show that there exist initial conditions such that the equation has no local solution in Lloc1(Rn).
KW - fractional heat equation
KW - fractional heat kernel
KW - local existence
KW - non-existence of solutions
UR - https://www.scopus.com/pages/publications/85041959199
U2 - 10.1515/fca-2017-0070
DO - 10.1515/fca-2017-0070
M3 - 文章
AN - SCOPUS:85041959199
SN - 1311-0454
VL - 20
SP - 1328
EP - 1337
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 6
ER -