Open AccessApproximation of a nonlinear fractal energy functional on varying Hilbert spaces
Author(s) -
Simone Creo,
Maria Rosaria Lancia,
Alejandro Vélez-Santiago,
Paola Vernole
Publication year - 2018
Publication title -
communications on pure and 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