| Abstract: |
| On a domain given as a tubular neighborhood of a graph, we consider a reaction-diffusion equation with the Neumann boundary condition. The domain converges to a line segment on each edge of the graph, while it shrinks faster to a point at each node. Then the equation is expected to be approximated by some one-dimensional limiting equation on the graph with appropriate matching conditions at the nodes. We formally derive the limiting equation and then show that it indeed approximates the original equation. |
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