Myopic models of population dynamics
      on infinite networks

Robert Carlson; Robert Carlson

doi:10.3934/nhm.2014.9.477

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

Robert Carlson ^{1
,}

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.
- Network reaction-diffusion problems,
- network population models,
- nonlinear diffusions
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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Abstract

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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