Dirichlet boundary valued problems for linear and nonlinear wave equations on arbitrary and fractal domains

We obtain the weak well-posedness results for linear strongly damped wave equation and nonlinear Westervelt on arbitrary three-dimensional domains with homogeneous Dirichlet boundary conditions. In R2, we prove in class of NTA or their limit domains, obtained as a sequences characterized by same geometrical constants. The nonhomogeneous condition is also treated Sobolev extension Rn d-set n−2<d<n preserving Markov's local inequality. For converging sequence sense characteristic functions, establish Mosco convergence functionals corresponding to formulations condition.