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

Abstract

The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in the largest natural class of Sobolev admissible non-smooth domains. In the framework of uniform domains in R^2 or R^3 we also validate the approximation of the solution of the Wester-velt equation on a fractal domain by the solutions on the prefractals using the Mosco convergence of the corresponding variational forms.

References in corpus (4)

• A new characterization of chord-arc domains
• Fractal snowflake domain diffusion with boundary and interior drifts
• Approximation of a compressible Navier-Stokes system by non-linear acoustical models
• Generalization of Rellich-Kondrachov theorem and trace compacteness in the framework of irregular and fractal boundaries