EXISTENCE, UNIQUENESS AND DECAY RATES FOR EVOLUTION EQUATIONS ON TREES
Leandro M. Del Pezzo, Carolina A. Mosquera, Julio, D. Rossi · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2014
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→∞. 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. 1.