Initial State Estimation Problems of Partial Differential Equations in Metric Graphs

In this paper, we deal with initial state estimation problems of the heat equation in metric graphs. Particularly, we aim to reveal proper assignments of observation points on metric graphs to identify the peak positions of initial states. From numerical simulations by singular value decompositions, it is predicted that a kind of symmetricity of metric graphs increases a minimum number of proper assignments of observation points. We also discuss relations between initial state estimation problems in partial differential equations in metric graphs and some problems in discrete graphs.