Comptes Rendus
no. 4
Khokhlov–Zabolotskaya–Kuznetsov type equation: nonlinear acoustics in heterogeneous media
[L'équation de type Khokhlov–Zabolotskaya–Kuznetsov : acoustique non linéaire dans un milieu hétérogène]

Présenté par : Évariste Sanchez-Palencia

Ilya Kostin1 ; Grigory Panasenko1 
1 Laboratory of Mathematics of the University of Saint-Etienne, (LaMUSE EA3989), université Jean-Monnet, 23, rue P. Michelon, 42023 Saint-Etienne, France
Comptes Rendus. Mécanique, Volume 334 (2006) no. 4, pp. 220-224.

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.

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.

Reçu le :
Accepté le :
Publié le :
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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