Existence, uniqueness and decay rates for evolution equations on trees

LEANDRO DEL PEZZO, CAROLINA MOSQUERA, JULIO ROSSI

PORTUGALIAE MATHEMATICA

European Mathematical Society

Año: 2014 vol. 71 p. 63 - 77

0032-5155

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.