  The weak well-posedness results of the strongly damped linear wave equation
and of the non linear Westervelt equation with homogeneous Dirichlet boundary
conditions are proved on arbitrary three dimensional domains or any two
dimensional domains which can be obtained by a limit of NTA domains
caractarized by the same geometrical constants. The two dimensional result is
obtained thanks to the Mosco convergence of the functionals corresponding to
the weak formulations for the Westervelt equation with the homogeneous
Dirichlet boundary condition. The non homogeneous Dirichlet condition is also
treated in the class of admissible domains composed on Sobolev extension
domains of $\mathbb{R}^n$ with a $d$-set boundary $n-1\leq d<n$ preserving
Markov's local inequality.The obtained Mosco convergence also alows to
approximate the solution of the Westervelt equation on an arbitrary domain by
solutions on a converging sequence of domains without additional conditions on
their boundary regularity in $\mathbb{R}^3$, or on a converging sequence of NTA
domains in $\mathbb{R}^2$.
