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, 21 . 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 apice for any given c > 0 and beta ∈ (0, 21 ).
Time-fractional equations with reaction terms: Fundamental solutions and asymptotics
Verzini, Gianmaria
2021-01-01
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, 21 . 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 apice for any given c > 0 and beta ∈ (0, 21 ).File in questo prodotto:
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