  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.
