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The weak well-posedness, with the mixed boundary conditions, of the stronglydamped linear wave equation and of the non linear Westervelt equation is provedin the largest natural class of Sobolev admissible non-smooth domains. In theframework of uniform domains in R^2 or R^3 we also validate the approximationof the solution of the Wester-velt equation on a fractal domain by thesolutions on the prefractals using the Mosco convergence of the correspondingvariational forms.

Mixed boundary valued problem for linear and nonlinear wave equations in domains with fractal boundaries