We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any α∈(0,1) to the same stationary state, the solution of the classic elliptic obstacle problem. The only thing which changes with α is the convergence speed. We also study the problem from the numerical point of view, comparing some finite different approaches, and showing the results of some tests. These results extend what recently proved in [1] for the case α=1.

On the time fractional heat equation with obstacle / Alberini, Carlo; Capitanelli, Raffaela; D'Ovidio, Mirko; FINZI VITA, Stefano. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - (2022). [10.1016/j.cam.2022.114470]

On the time fractional heat equation with obstacle

Carlo Alberini;Raffaela Capitanelli
;
Mirko D’Ovidio;Stefano Finzi Vita
2022

Abstract

We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any α∈(0,1) to the same stationary state, the solution of the classic elliptic obstacle problem. The only thing which changes with α is the convergence speed. We also study the problem from the numerical point of view, comparing some finite different approaches, and showing the results of some tests. These results extend what recently proved in [1] for the case α=1.
Degenerate parabolic problems; Finite difference methods; Fractional derivatives and integrals; Free boundary problems
01 Pubblicazione su rivista::01a Articolo in rivista
On the time fractional heat equation with obstacle / Alberini, Carlo; Capitanelli, Raffaela; D'Ovidio, Mirko; FINZI VITA, Stefano. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - (2022). [10.1016/j.cam.2022.114470]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1649596
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