Existence, uniqueness and decay rates for evolution equations on trees
Analysis of PDEs
2014-03-25 v2
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
@article{arxiv.1309.7634,
title = {Existence, uniqueness and decay rates for evolution equations on trees},
author = {Leandro M. Del Pezzo and Carolina A. Mosquera and Julio D. Rossi},
journal= {arXiv preprint arXiv:1309.7634},
year = {2014}
}
Comments
11 pages. Keywords: Evolution equations, averaging operators, decay estimates. arXiv admin note: text overlap with arXiv:1303.6521