Extinction and positivity of the solutions of the heat equations with absorption on networks
Extinction and positivity of the solutions of the heat equations with absorption on networks
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DOI：
10.1016/j.jmaa.2011.03.006
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发表时间：
2011-08
影响因子：
1.3
通讯作者：
Yun-Sung Chung;Young-S. Lee;Soon‐Yeong Chung
中科院分区：
文献类型：
--
作者：
Yun-Sung Chung;Young-S. Lee;Soon‐Yeong Chung
在本文中，我们提出了下列带吸收的半线性热方程ut=Δu−uqwithq >1的离散版本，它被称为网络中带吸收的ω-热方程。利用离散拉普拉斯算子Δωon（加权图），定义了网络上具有吸收的ω-热方程，并给出了它们的物理解释。主要研究初始数据为非负且边界数据消失的方程的非平凡解的大时间行为。证明了解u（x,t）在t趋于+∞时的渐近性质强烈依赖于q−1的符号。
In this paper, we propose a discrete version of the following semilinear heat equation with absorption ut=Δu−uqwith q>1, which is said to be the ω-heat equation with absorption on a network. Using the discrete Laplacian operator Δωon a weighted graph, we define the ω-heat equations with absorption on networks and give their physical interpretations. The main concern is to investigate the large time behaviors of nontrivial solutions of the equations whose initial data are nonnegative and the boundary data vanish. It is proved that the asymptotic behaviors of the solutions u(x,t) as t tends to +∞ strongly depend on the sign of q−1.