Comptes Rendus
Khokhlov–Zabolotskaya–Kuznetsov type equation: nonlinear acoustics in heterogeneous media
Comptes Rendus. Mécanique, Volume 334 (2006) no. 4, pp. 220-224.

The KZK type equation introduced in this Note differs from the traditional form of the KZK model known in acoustics by the assumptions on the nonlinear term. For this modified form, a global existence and uniqueness result is established for the case of non-constant coefficients. Afterwards the asymptotic behaviour of the solution of the KZK type equation with rapidly oscillating coefficients is studied.

L'équation de type KZK introduit dans cette Note est une version modifiée du modèle KZK connu en acoustique (ces modifications concernent les hypothèses sur le terme non linéaire). Pour cette forme modifiée, un résultat d'existence et unicité globales est établi dans le cas des coefficients variables. Ensuite le comportement asymptotique de la solution de l'équation de type KZK avec les coefficients rapidement oscillants est étudié.

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DOI: 10.1016/j.crme.2006.01.010
Keywords: Acoustics, Nonlinear acoustics, KZK equation, Homogenization
Mot clés : Acoustique, Acoustique non linéaire, Équation KZK, Homogéneisation

Ilya Kostin 1; Grigory Panasenko 1

1 Laboratory of Mathematics of the University of Saint-Etienne, (LaMUSE EA3989), université Jean-Monnet, 23, rue P. Michelon, 42023 Saint-Etienne, France
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Ilya Kostin; Grigory Panasenko. Khokhlov–Zabolotskaya–Kuznetsov type equation: nonlinear acoustics in heterogeneous media. Comptes Rendus. Mécanique, Volume 334 (2006) no. 4, pp. 220-224. doi : 10.1016/j.crme.2006.01.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.01.010/

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