Ricerc@Sapienza

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.