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

We obtain the weak well-posedness results for the linear strongly damped wave equation and the nonlinear Westervelt equation on arbitrary three-dimensional domains with homogeneous Dirichlet boundary conditions. In R2, we prove the well-posedness in the class of NTA domains or their limit domains, obtained as a limit of sequences of NTA domains, characterized by the same geometrical constants. The nonhomogeneous Dirichlet condition is also treated for Sobolev extension domains of Rn with a d-set boundary n−2更多