Uniform blow‐up profile and boundary behaviour for a non‐local reaction–diffusion equation with critical damping
Uniform blow‐up profile and boundary behaviour for a non‐local reaction–diffusion equation with critical damping
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DOI：
10.1002/mma.567
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发表时间：
2004-10
影响因子：
2.9
通讯作者：
P. Souplet
中科院分区：
文献类型：
--
作者：
P. Souplet
考虑一类带积分源项和局部阻尼的非局部反应扩散方程的Dirichlet问题。从以前的工作中可以知道，对于亚临界阻尼，爆破是全局的，并且爆破轮廓在域的所有紧凑子集上是均匀的。在本文中，我们讨论了临界情况。结果显示爆炸侧写还是一样的我们还计算了急剧的爆破速率，发现与亚临界情况不同，爆破速率揭示了阻尼项的影响。
We consider the Dirichlet problem for a non‐local reaction–diffusion equation with integral source term and local damping involving power non‐linearities. It is known from previous work that for subcritical damping, the blow‐up is global and the blow‐up profile is uniform on all compact subsets of the domain. In this paper, we address the critical case. It turns out that the blow‐up profile is still uniform. Also we compute the sharp blow‐up rate and we find that, unlike in the subcritical case, the blow‐up rate reveals the influence of the damping term.