Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers; Anna Rozanova-Pierrat; Vladimir Khodygo

doi:10.3934/dcds.2020179

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers, Anna Rozanova-Pierrat, Vladimir Khodygo^*

^*Corresponding author for this work

Department of Life Sciences

Paris-Saclay University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

21 Downloads (Pure)

Abstract

We relate together different models of non linear acoustic in thermo-elastic 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 L² 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.

Original language	English
Pages (from-to)	4231-4258
Number of pages	28
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	40
Issue number	7
Early online date	27 Apr 2020
DOIs	https://doi.org/10.3934/dcds.2020179
Publication status	Published - 01 Jul 2020

Keywords

Approximations
Kuznetsov
KZK
Non-linear acoustic
NPE
Westervelt equations

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title = "Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation",

abstract = "We relate together different models of non linear acoustic in thermo-elastic 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 L2 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.",

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AU - Dekkers, Adrien

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AU - Khodygo, Vladimir

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Y1 - 2020/7/1

N2 - We relate together different models of non linear acoustic in thermo-elastic 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 L2 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.

AB - We relate together different models of non linear acoustic in thermo-elastic 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 L2 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.

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Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

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Keywords

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