Approximation of a nonlinear fractal energy functional on varying Hilbert spaces

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.