JournalspmVol. 71, No. 1pp. 63–77

Existence, uniqueness and decay rates for evolution equations on trees

  • Leandro M. Del Pezzo

    Universidad Torcuato di Tella, C. A. de Buenos Aires, Argentina
  • Carolina A. Mosquera

    Universidad de Buenos Aires, Argentina
  • Enrique Jordá

    Universitat Politècnica de València, Alcoy (Alicante), Spain
Existence, uniqueness and decay rates for evolution equations on trees cover
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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 tt\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.

Cite this article

Leandro M. Del Pezzo, Carolina A. Mosquera, Enrique Jordá, Existence, uniqueness and decay rates for evolution equations on trees. Port. Math. 71 (2014), no. 1, pp. 63–77

DOI 10.4171/PM/1941