MODELS OF NONLINEAR ACOUSTICS VIEWED AS AN APPROXIMATION OF THE KUZNETSOV EQUATION

Abstract : 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. In the aim 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) were obtained.
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https://hal.archives-ouvertes.fr/hal-02134311
Contributor : Adrien Dekkers <>
Submitted on : Monday, May 20, 2019 - 3:05:19 PM
Last modification on : Thursday, June 6, 2019 - 11:26:01 AM

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  • HAL Id : hal-02134311, version 1

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Adrien Dekkers, Vladimir Khodygo, Anna Rozanova-Pierrat. MODELS OF NONLINEAR ACOUSTICS VIEWED AS AN APPROXIMATION OF THE KUZNETSOV EQUATION. 2019. ⟨hal-02134311⟩

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