MODELS OF NONLINEAR ACOUSTICS VIEWED AS APPROXIMATIONS OF THE KUZNETSOV EQUATION

被引：6

作者：

Dekkers, Adrien ^{[1
]}

Rozanova-Pierrat, Anna ^{[1
]}

Khodygo, Vladimir ^{[2
]}

机构：

[1] Univ Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, France

[2] Aberystwyth Univ, Inst Biol Environm & Rural Sci, Penglais Campus, Aberystwyth SY23 3DA, Ceredigion, Wales

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 07期

关键词：

Non-linear acoustic; approximations; Kuznetsov; KZK; NPE and Westervelt equations; NAVIER-STOKES EQUATIONS; BOUNDARY-VALUE-PROBLEMS; WAVE-EQUATION; MULTIDIMENSIONAL FLOWS; WELL-POSEDNESS; CAUCHY-PROBLEM; LIFE-SPAN; DERIVATION; TUTORIAL;

D O I：

10.3934/dcds.2020179

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We relate together different models of non linear acoustic in thermoelastic media as the Kuznetsov equation, theWestervelt equation, the KhokhlovZabolotskaya-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.

引用

页码：4231 / 4258

页数：28

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[1] DISTORTION AND HARMONIC-GENERATION IN THE NEARFIELD OF A FINITE-AMPLITUDE SOUND BEAM [J].