%0 Journal Article %T Existence, uniqueness and decay rates for evolution equations on trees %A Leandro M. Del Pezzo %A Carolina A. Mosquera %A Julio D. Rossi %J Mathematics %D 2013 %I arXiv %R 10.4171/PM/1941 %X 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 $t\to \infty$. 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. %U http://arxiv.org/abs/1309.7634v2