论文标题
标量非局部一维抛物线抛物线问题的平衡的稳定性和平衡性
Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem
论文作者
论文摘要
在这项工作中，我们介绍了标量非局部一维准线性抛物线问题的稳定性和均衡性的结果。我们表明，著名的Chafee-Infante方程的这个非本地版本与本地版本有些相似。但是，其非局部特性需要对相关线性操作员的光谱进行精细分析，比本地情况要付出更多。对于这种准线性模型，表明平衡的鞍点特性。
In this work, we present results on stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem. We show that this nonlocal version of the well-known Chafee-Infante equation bares some resemblance with the local version. However, its nonlocal characteristc requires a fine analysis of the spectrum of the associated linear operators, a lot more ellaborated than the local case. The saddle point property of equilibria is shown to hold for this quasilinear model.
