English

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, 12\frac12. 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~ctβct^\beta for any given~c>0c>0 and~β(0,12)\beta\in\left(0,\frac12\right).

Keywords

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}
}