Approximation of a nonlinear fractal energy functional on varying Hilbert spaces | Zendy

Simone Creo | Zendy; Maria Rosaria Lancia | Zendy; Alejandro Vélez-Santiago | Zendy; Paola Vernole | Zendy

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Approximation of a nonlinear fractal energy functional on varying Hilbert spaces

Author(s) -

Simone Creo,

Maria Rosaria Lancia,

Alejandro Vélez-Santiago,

Paola Vernole

Publication year - 2017

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2018035

Subject(s) - fractal , mathematics , semigroup , uniqueness , hilbert space , fractal derivative , mathematical analysis , nonlinear system , boundary (topology) , domain (mathematical analysis) , energy functional , convergence (economics) , limit (mathematics) , pure mathematics , fractal dimension , fractal analysis , physics , quantum mechanics , economics , economic growth

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

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