Observability for the Heat Equation in Equilateral Metric Graphs

This paper deals with the observability problems of distributed parameter systems, in particular the heat equation in metric graphs. We derive the necessary and sufficient condition for observability for the heat equation with the Kirchhoff conditions in equilateral metric graphs. In some numerical simulations, we successfully obtain true initial states by choosing observation points on metric graphs with satisfying the derived necessary and sufficient condition for observability.