Existence, uniqueness and decay rates for evolution equations on trees
Leandro M. Del Pezzo
Universidad de Buenos Aires, ArgentinaCarolina A. Mosquera
Universidad de Buenos Aires, ArgentinaJulio D. Rossi
Universidad de Alicante, Spain
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Abstract
We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as . It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.
Cite this article
Leandro M. Del Pezzo, Carolina A. Mosquera, Julio D. Rossi, Existence, uniqueness and decay rates for evolution equations on trees. Port. Math. 71 (2014), no. 1, pp. 63–77
DOI 10.4171/PM/1941