Journal of the
Korean Mathematical Society JKMS

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $$ \sum_{n=0}^l c_n \partial_t^n u(x,t)-\rho(x)\Delta_\omega u(x,t)=H(x,t), $$ defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

Keywords: discrete Laplacian, evolution equations, inverse problems

MSC numbers: 35R02, 35K20, 35R30