Asymptotics for Time-Fractional Venttsel’ Problems in Fractal Domains

Fractal and Fractional

article

Raffaela Capitanelli¹  Simone Creo¹  Maria Rosaria Lancia¹ 

[1] Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma

关键词: fractional Caputo time derivative;    Venttsel’ problems;    fractal domains;    asymptotic behavior;    varying Hilbert spaces;    resolvent families35R11;    26A33;    35B40;    28A80;   

DOI  :  10.3390/fractalfract7060479

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY