Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Abstract

We relate together different models of non linear acoustic in thermoelastic 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.

Models of nonlinear acoustics viewed as an approximation of the Navier–Stokes and Euler compressible isentropic systems

“…The most known nonlinear acoustic models, which we consider in this paper, are 1. the Kuznetsov equation (see Eq. (11) and Eq. (21)), which is actually a quasi-linear (damped) wave equation, initially introduced by Kuznetsov [23] for the velocity potential, see also Refs.…”

“…But the KZK-and NPE-paraxial approximations allow to have the approximate equations with all terms of the same order, i.e. the KZK and NPE equations [11]. The well-posedness results for boundary value problems for the Kuznetsov equation are given in Refs.…”