We find a d'Alembert type formula for the solution of the Cauchy problem for the wave equation on finite weighted networks. We also discuss the periodicity in time of the solution in terms of the spectrum of the discrete graph associated with the network and finally we present two significant examples to illustrate and clarify the general analysis
Cattaneo, C., Fontana, L. (2003). D'Alembert formula on finite one-dimensional networks. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 284(2), 403-424 [10.1016/S0022-247X(02)00392-X].
D'Alembert formula on finite one-dimensional networks
Fontana, L
2003
Abstract
We find a d'Alembert type formula for the solution of the Cauchy problem for the wave equation on finite weighted networks. We also discuss the periodicity in time of the solution in terms of the spectrum of the discrete graph associated with the network and finally we present two significant examples to illustrate and clarify the general analysis
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