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Networks and Heterogeneous Media

2014, Volume 9, Issue 3: 477-499. doi: 10.3934/nhm.2014.9.477
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Myopic models of population dynamics on infinite networks

  • 1.
    Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80918
  • Received: 01 November 2013 Revised: 01 June 2014

  • Primary: 34B45.

  • Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions which are flat at infinity. The algebra is associated with a compactification of the network which facilitates the description of spatial asymptotics. Diffusive effects disappear at infinity, greatly simplifying the remote dynamics. Accelerated diffusion models with conventional eigenfunction expansions are constructed to provide opportunities for finite dimensional approximation.

    Citation: Robert Carlson. Myopic models of population dynamics on infinite networks[J]. Networks and Heterogeneous Media, 2014, 9(3): 477-499. doi: 10.3934/nhm.2014.9.477

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  • Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions which are flat at infinity. The algebra is associated with a compactification of the network which facilitates the description of spatial asymptotics. Diffusive effects disappear at infinity, greatly simplifying the remote dynamics. Accelerated diffusion models with conventional eigenfunction expansions are constructed to provide opportunities for finite dimensional approximation.


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