## Abstract

We relate together different models of non linear acoustic in thermo-elastic 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.

Original language | English |
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Pages (from-to) | 4231-4258 |

Number of pages | 28 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Volume | 40 |

Issue number | 7 |

Early online date | 27 Apr 2020 |

DOIs | |

Publication status | Published - 01 Jul 2020 |

## Keywords

- Approximations
- Kuznetsov
- KZK
- Non-linear acoustic
- NPE
- Westervelt equations