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arXiv · 2106.02911

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

Xueli Bai·Fang Li·Xiaoliu Wang
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Abstract

This paper studies a type of degenerate parabolic problem with nonlocal term \begin{equation*} \begin{cases} u_t=u^p(u_{xx}+u-\bar{u}) & 0 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 $t\rightarrow +\infty$.

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Xueli Bai, Fang Li, Xiaoliu Wang. 2021-06-05. Global dynamics of a parabolic type equation arising from the curvature flow. https://doi.org/10.1088/1361-6544%2Fac9a95

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