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

Adrien Dekkers (1) , Anna Rozanova-Pierrat (1, 2) , Alexander Teplyaev (3)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
3 UCONN - University of Connecticut

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.

Mots clés: Fractals; Wave equation; Westervelt equation; Quasilinear second-order hyperbolic equations; Mosco convergence

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Adrien Dekkers, Anna Rozanova-Pierrat, Alexander Teplyaev. Mixed boundary valued problem for linear and nonlinear wave equations in domains with fractal boundaries. Calculus of Variations and Partial Differential Equations, 2022, 61 (2), pp.75. ⟨10.1007/s00526-021-02159-3⟩. ⟨hal-02514311⟩