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arXiv · 1903.11939

Time-fractional equations with reaction terms: fundamental solutions and asymptotics

Serena Dipierro·Benedetta Pellacci·Enrico Valdinoci·Gianmaria Verzini
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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, $\frac12$. 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~$ct^\beta$ for any given~$c>0$ and~$\beta\in\left(0,\frac12\right)$.

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Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci, Gianmaria Verzini. 2019-03-28. Time-fractional equations with reaction terms: fundamental solutions and asymptotics. https://arxiv.org/abs/1903.11939

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