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We relate together different models of non linear acoustic in thermo-ellasticmedia as the Kuznetsov equation, the Westervelt equation, theKhokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressivewave Equation (NPE) and estimate the time during which the solutions of thesemodels keep closed in the L 2 norm. The KZK and NPE equations are considered asparaxial approximations of the Kuznetsov equation. The Westervelt equation isobtained as a nonlinear approximation of the Kuznetsov equation. Aiming tocompare the solutions of the exact and approximated systems in foundapproximation domains the well-posedness results (for the Kuznetsov equation ina half-space with periodic in time initial and boundary data) are obtained.

Models of Nonlinear Acoustics Viewed as Approximations of the Kuznetsov Equation