MODELS OF NONLINEAR ACOUSTICS VIEWED AS APPROXIMATIONs OF THE KUZNETSOV EQUATION

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

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

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

Domaines: Equations aux dérivées partielles [math.AP]

Adrien Dekkers, Vladimir Khodygo, Anna Rozanova-Pierrat. MODELS OF NONLINEAR ACOUSTICS VIEWED AS APPROXIMATIONs OF THE KUZNETSOV EQUATION. Discrete and Continuous Dynamical Systems - Series A, In press. ⟨hal-02134311v1⟩