Hawking Evaporation of Einstein-Gauss-Bonnet AdS Black Holes in $D\geqslant 4$ dimensions.

Einstein-Gauss-Bonnet theory is a string generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help solving black hole singularity problem. In this work we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein-Gauss-Bonnet gravity in various spacetime dimensions with both positive and negative couping constant $\alpha$. By summarizing the asymptotic behavior of evaporation process, we find the lifetime of the black holes is dimensional dependent. For $\alpha>0$, in $D\geqslant6$ cases, the black holes will be completely evaporated in a finite time, which resemble the Schwarzschild-AdS case in Einstein gravity. While in $D=4,5$ cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $\alpha>0,D=4,5$ will solve the terminal temperature divergent problem of Schwarzschild-AdS case. For $\alpha<0$, in all dimensions, the black hole will always spend a finite time to an minimal mass corresponding to a smallest horizon radius $r_{min}=\sqrt{2|\alpha|}$ which coincide with an additional singularity. This phenomenon may violate the cosmic censorship, and it implies that there may exist constraint conditions to the choice of couping constant.