Discrete evolution equations on networks and a unique identifiability of their weights
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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.
Abstract
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.
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