Asymptotics for Time-Fractional Venttsel’ Problems in Fractal Domains

In this study, we consider fractional-in-time Venttsel’ problems in fractal domains of the Koch type. Well-posedness and regularity results are given. In view of numerical approximation, we consider the associated approximating pre-fractal problems. Our main result is the convergence of the solution...

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Bibliographic Details
Published in:Fractal and fractional 2023-06, Vol.7 (6), p.479
Main Authors: Capitanelli, Raffaela, Creo, Simone, Lancia, Maria Rosaria
Format: Article
Language:English
Subjects:
Approximation
asymptotic behavior
Boundary conditions
Cauchy problems
Convergence
Domains
fractal domains
Fractals
fractional Caputo time derivative
Hilbert space
resolvent families
varying Hilbert spaces
Venttsel’ problems
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Summary:In this study, we consider fractional-in-time Venttsel’ problems in fractal domains of the Koch type. Well-posedness and regularity results are given. In view of numerical approximation, we consider the associated approximating pre-fractal problems. Our main result is the convergence of the solutions of such problems towards the solution of the fractional-in-time Venttsel’ problem in the corresponding fractal domain. This is achieved via the convergence (in the Mosco–Kuwae–Shioya sense) of the approximating energy forms in varying Hilbert spaces.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7060479