Journal Articles Calculus of Variations and Partial Differential Equations Year : 2022

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.
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Dates and versions

hal-02514311 , version 1 (21-03-2020)

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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⟩
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