Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers (1) , Anna Rozanova-Pierrat (1) , Vladimir Khodygo (2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 Aberystwyth University

We relate together different models of non linear acoustic in thermo-ellastic media as the Kuznetsov equation, the Westervelt equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) and estimate the time during which the solutions of these models keep closed in the L 2 norm. The KZK and NPE equations are considered as paraxial approximations of the Kuznetsov equation. The Westervelt equation is obtained as a nonlinear approximation of the Kuznetsov equation. Aiming to compare the solutions of the exact and approximated systems in found approximation domains the well-posedness results (for the Kuznetsov equation in a half-space with periodic in time initial and boundary data) are obtained.

Mots clés: Non-linear acoustic; approximations; Kuznetsov; KZK; NPE; Westervelt equations

Domaines: Equations aux dérivées partielles [math.AP]

Adrien Dekkers, Anna Rozanova-Pierrat, Vladimir Khodygo. Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 A (7), pp.4231-4258. ⟨10.3934/dcds.2020179⟩. ⟨hal-02134311v2⟩