Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations
Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations
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DOI：
10.3934/dcds.2008.20.1123
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发表时间：
2008
影响因子：
1.1
通讯作者：
X. Xing;Yaping Wu
中科院分区：
文献类型：
--
作者：
X. Xing;Yaping Wu
本文讨论了一类p次Fisher方程在临界速度下旅行前沿解的稳定性。通过详细的谱分析和次超解方法，我们首先证明了具有临界速度的旅行锋解在一些指数加权空间中是全局指数稳定的。此外，利用Evans函数方法、适当的空间分解和详细的半群衰减估计，我们可以证明临界速度波在某些多项式加权空间中是局部渐近稳定的，从而验证了数值模拟得到的一些渐近现象。
This paper is concerned with the stability of the traveling front solutions with critical speeds for a class of $p$-degree Fisher-type equations. By detailed spectral analysis and sub-supper solution method, we first show that the traveling front solutions with critical speeds are globally exponentially stable in some exponentially weighted spaces. Furthermore by Evans's function method, appropriate space decomposition and detailed semigroup decaying estimates, we can prove that the waves with critical speeds are locally asymptotically stable in some polynomially weighted spaces, which verifies some asymptotic phenomena obtained by numerical simulations.