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Approximation of a nonlinear fractal energy functional on varying Hilbert spaces

  • * Corresponding author: Maria Rosaria Lancia

    * Corresponding author: Maria Rosaria Lancia 
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  • We study a quasi-linear evolution equation with nonlinear dynamical 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 uniqueness 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 convergence of the energy functionals adapted by Tölle to the nonlinear framework in varying Hilbert spaces.

    Mathematics Subject Classification: Primary:35K, 28A80;Secondary:37L05, 31C25.


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  • Figure 1.  The Koch snowflake

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