We study a quasi-linear evolution equation with nonlinear dynami- cal boundary conditions in a two dimensional domain with Koch-type fractal boundary. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uni- queness results via standard semigroup approach, we prove that the pre-fractal solutions converge in a suitable sense to the limit fractal one via the Mosco con- vergence of the energy functionals adapted by T ̈olle to the nonlinear framework in varying Hilbert spaces.

Approximation of a nonlinear fractal energy functional on varying hilbert spaces / Creo, Simone; Lancia, Maria Rosaria; Velez-santiago, A.; Vernole, Paola. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 17:(2018), pp. 647-669. [doi:10.3934/cpaa.2018035]

Approximation of a nonlinear fractal energy functional on varying hilbert spaces

CREO, SIMONE
Membro del Collaboration Group
;
Maria Rosaria Lancia
Membro del Collaboration Group
;
Paola Vernole
Membro del Collaboration Group
2018

Abstract

We study a quasi-linear evolution equation with nonlinear dynami- cal boundary conditions in a two dimensional domain with Koch-type fractal boundary. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uni- queness results via standard semigroup approach, we prove that the pre-fractal solutions converge in a suitable sense to the limit fractal one via the Mosco con- vergence of the energy functionals adapted by T ̈olle to the nonlinear framework in varying Hilbert spaces.
Asymptotic behavior, Venttsel’ problems, nonlinear energy forms, fractal domains, trace theorems, varying Hilbert spaces, p-Laplacian, nonlinear semigroups.
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Approximation of a nonlinear fractal energy functional on varying hilbert spaces / Creo, Simone; Lancia, Maria Rosaria; Velez-santiago, A.; Vernole, Paola. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 17:(2018), pp. 647-669. [doi:10.3934/cpaa.2018035]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1015605
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