On global existence for the Gierer-Meinhardt system
On global existence for the Gierer-Meinhardt system
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DOI：
10.3934/dcds.2015.35.583
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发表时间：
2014-08
影响因子：
1.1
通讯作者：
Henghui Zou
中科院分区：
文献类型：
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作者：
Henghui Zou
我们考虑具有齐次Neumann边界条件的有界光滑域$\Omega\subset\mathbb{R}^n$（$n\ge1$）上的Giererer-Meinhardt系统（1.1），如下所示。对于适当的指数a，B，c和d，我们建立了全局存在的充分条件.本文的定理1.1与文献[6]的定理1.2相结合，揭示了初值对整体解存在性和有限时间爆破的影响的一个经典现象。这一工作是我们早先关于Gierer-Meinhardt系统的结果[6]的继续。Gierer-Meinhardt系统在[1]中被引入来模拟生态系统中模式形成中的激活剂-抑制剂系统。
We consider the Gierer-Meinhardt system (1.1), shown below, on a bounded smooth domain $\Omega\subset\mathbb{R}^n$ ($n\ge1$) with a homogeneous Neumann boundary condition. For suitable exponents $a$, $b$, $c$ and $d$, we establish certain sufficient conditions for global existence. Theorem 1.1 here, combined with Theorem 1.2 of [6], implies a classical phenomenon on the effect of the initial data on global existence and finite time blow-up. This work is a continuation of our earlier result [6] for the Gierer-Meinhardt system. The Gierer-Meinhardt system was introduced in [1] to model activator-inhibitor systems in pattern formation in ecological systems.