arXiv Analytics

Sign in

arXiv:1309.7634 [math.AP]AbstractReferencesReviewsResources

Existence, uniqueness and decay rates for evolution equations on trees

Leandro M. Del Pezzo, Carolina A. Mosquera, Julio D. Rossi

Published 2013-09-29, updated 2014-03-24Version 2

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.

Comments: 11 pages. Keywords: Evolution equations, averaging operators, decay estimates. arXiv admin note: text overlap with arXiv:1303.6521
Journal: Portugaliae Mathematica, Vol. 71, Fasc. 1, 2014, 63-77
Categories: math.AP
Subjects: 35B40, 35K55, 91A22
Related articles: Most relevant | Search more
arXiv:2104.12833 [math.AP] (Published 2021-04-26)
Coupled local/nonlocal models in thin domains
arXiv:math/0512629 [math.AP] (Published 2005-12-29)
Existence and uniqueness of solutions for a nonlocal parabolic thermistor-type problem
arXiv:2103.14751 [math.AP] (Published 2021-03-26)
Recovering the initial condition in the One-Phase Stefan problem

Links

Toolbox