非局部柯西问题弱解的衰减速度

摘要

In this paper,the asymptotic behavior of the weak solution (ut)t≥0 to the non-local Cauchy problems as stated in (1) is considered.Only using lower bounds of jumping kernel J(x,y) for large ｜x-y｜,it is obtained that ‖ut‖p ≤ c(t)‖u0‖q with any 1 ≤ q ＜ p ＜ ∞ and large t.Explicit and sharp formulas for c(t) are also given.%考虑如(1)所示的非局部柯西问题弱解(ut)t≥o的渐近性质.仅利用跳核J(x,y)当｜x-y｜充分大时下界的性质,本文证明了对于任意1≤q＜p＜∞及充分大t,‖ut‖p≤c(t)‖uo‖q成立,同时给出c(t)的最优显示估计式.