Initial state estimation from limited observations of the heat equation in metric graphs

This paper deals with initial state estimation problems of the heat equation in equilateral metric graphs being admitted to have cycles. Particularly, we are concerned with suitable placements of observation points in order to uniquely determine the initial state from observation data. We give a necessary and sufficient condition for suitable placements of observation points, and such suitable placements are determined from transition matrices of metric graphs. From numerical simulations, we confirm effectiveness of a necessary and sufficient condition.

Automated summary

This paper tackles the issue of initial state estimation for the heat equation in equilateral metric graphs with cycles. The focus is on determining suitable placements of observation points in order to uniquely determine the initial state from observation data. The paper provides a necessary and sufficient condition for these suitable placements, and verifies their effectiveness through numerical simulations.