Global dynamics of a parabolic type equation arising from the curvature flow

Abstract

This paper studies a type of degenerate parabolic problem with nonlocal termwhere p > 1, a > 0. In this paper, the classification of the finite-time blowup/global existence phenomena based on the associated energy functional and explicit expression of all nonnegative steady states are demonstrated. Moreover, we combine the applications of Lojasiewicz-Simon inequality and energy estimates to derive that any bounded solution with positive initial data converges to some steady state as t → +∞.