Abstract

In this paper, we obtain bounds for the decay rate for solutions to the nonlocal problem partial derivative tu(t,x) = integral(Rn) J(x,y)[u(t,y) - u(t,x)]dy. Here we deal with hounded keniels J but with polynomial tails, that, is, we assume a lower bound of the form J (x,y) >= c(1)-x - y-(-(n+2 sigma)), for -x - y- > c(2). Our estimates takes the form --u(t)--(Lq(Rn)) <= Ct(-(n/2 sigma)(1-1/q)) for t large.