Diffusion in Networks with Time-Dependent Transmission Conditions
Diffusion in Networks with Time-Dependent Transmission Conditions
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DOI：
10.1007/s00245-013-9225-1
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发表时间：
2013-03
影响因子：
1.8
通讯作者：
W. Arendt;Dominik Dier;Marjeta Kramar Fijavž-Marjeta-Kramar Fijavž-147510673
中科院分区：
文献类型：
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作者：
W. Arendt;Dominik Dier;Marjeta Kramar Fijavž-Marjeta-Kramar Fijavž-147510673
我们研究了在图的顶点受非自治Kirchhoff条件支配的网络中的扩散问题。此外，扩散系数可能依赖于时间。我们首先用形式方法证明了一个关于解的存在唯一性的结果。我们的主要结果涉及解决方案的长期行为。在电导率和扩散系数匹配的情况下(这样质量是守恒的)，我们证明了解以指数方式快速收敛到平衡点。在其他一些情况下，我们也证明了收敛到一个特解。
We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form methods. Our main results concern the long-term behavior of the solution. In the case when the conductivity and the diffusion coefficients match (so that mass is conserved) we show that the solution converges exponentially fast to an equilibrium. We also show convergence to a special solution in some other cases.