Time-fractional equations with reaction terms: fundamental solutions and asymptotics
Analysis of PDEs
2019-03-29 v1
Abstract
We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional exponent is equal to, or larger than, . In this situation, we prove that the speed of invasion of the fundamental solution is at least `almost of square root type', namely it is larger than~ for any given~ and~.
Cite
@article{arxiv.1903.11939,
title = {Time-fractional equations with reaction terms: fundamental solutions and asymptotics},
author = {Serena Dipierro and Benedetta Pellacci and Enrico Valdinoci and Gianmaria Verzini},
journal= {arXiv preprint arXiv:1903.11939},
year = {2019}
}