Diffusion in Networks with Time-Dependent Transmission Conditions

作者：Arendt Wolfgang; Dier Dominik; Fijavz Marjeta Kramar^*

来源：Applied Mathematics and Optimization, 2014, 69(2): 315-336.

DOI：10.1007/s00245-013-9225-1

• Time-dependent networks
• Diffusion
• Non-autonomous evolution equations
• Sesquilinear forms
• Asymptotic behavior

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.

• 出版日期2014-4