Diffusion in networks with time-dependent transmission conditions
Analysis of PDEs
2014-03-12 v2 Functional Analysis
Abstract
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.
Cite
@article{arxiv.1303.4951,
title = {Diffusion in networks with time-dependent transmission conditions},
author = {Wolfgang Arendt and Dominik Dier and Marjeta Kramar Fijavž},
journal= {arXiv preprint arXiv:1303.4951},
year = {2014}
}
Comments
corrected typos, references removed, revised Lemma A.3. Appl. Math. Optim. (2013)