Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers, ,Laboratory Mathématiques et Informatique pour la Complexité et les Systèmes, CentraleSupélec, Univérsité Paris-Saclay, Campus de Gif-sur-Yvette, Plateau de Moulon, 3 rue Joliot Curie, 91190 Gif-sur-Yvette, France, Anna Rozanova-Pierrat, Vladimir Khodygo, ,Institute of Biological, Environmental and Rural Sciences, Aberystwyth University, Penglais Campus, Aberystwyth, Ceredigion, Wales, SY23 3DA, United Kingdom
2020 Discrete and Continuous Dynamical Systems. Series A  
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
more » ... etsov 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. 2010 Mathematics Subject Classification. Primary: 35L15, 35L71; Secondary: 35B45.
doi:10.3934/dcds.2020179 fatcat:ojeclnpqxbajnl5siaingq6shy