Existence, uniqueness and decay rates for evolution equations on trees

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 $t\to \infty$. 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.

11 pages. Keywords: Evolution equations, averaging operators, decay estimates. arXiv admin note: text overlap with arXiv:1303.6521

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