https://neckpinch.com/authors/xueli-bai/New arXiv papers by Xueli Bai, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.02911/arxiv:2106.02911Sat, 05 Jun 2021 00:00:00 GMTXueli Bai, Fang Li, Xiaoliu Wang — This paper studies a type of degenerate parabolic problem with nonlocal term \beginequation* \begincases u_t=u^p(u_xx+u-\baru) & 0<t<T_{\max},\ 0<x<a, u_x(0,t)=u_x(a,t)=0 & 0<t<T_{\max}, u(x,0)=u_0(x) & 0<x<a, \endcases \endequation* where 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→ +∞.Other curvature flowsSingularitiesLong-time existence & convergence