Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers; Anna Rozanova-Pierrat; Vladimir Khodygo

doi:10.3934/dcds.2020179

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers, Anna Rozanova-Pierrat, Vladimir Khodygo^*

^*Awdur cyfatebol y gwaith hwn

Adran y Gwyddorau Bywyd

Université Paris Sud

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

7 Dyfyniadau (Scopus)

31 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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 L² 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.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	4231-4258
Nifer y tudalennau	28
Cyfnodolyn	Discrete and Continuous Dynamical Systems- Series A
Cyfrol	40
Rhif cyhoeddi	7
Dyddiad ar-lein cynnar	27 Ebr 2020
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.3934/dcds.2020179
Statws	Cyhoeddwyd - 01 Gorff 2020

Mynediad at Ddogfen

10.3934/dcds.2020179Trwydded: Cyhoeddwr

1078-0947_2020_7_4231Fersiwn derfynol wedi’i chyhoeddi, 467 KB

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Link to publication in Scopus

Dyfynnu hyn

@article{fa062e1e8f874f78a53efb979427b4bc,

title = "Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation",

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 L2 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.",

keywords = "Approximations, Kuznetsov, KZK, Non-linear acoustic, NPE, Westervelt equations",

author = "Adrien Dekkers and Anna Rozanova-Pierrat and Vladimir Khodygo",

year = "2020",

month = jul,

day = "1",

doi = "10.3934/dcds.2020179",

language = "English",

volume = "40",

pages = "4231--4258",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "7",

}

TY - JOUR

T1 - Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

AU - Dekkers, Adrien

AU - Rozanova-Pierrat, Anna

AU - Khodygo, Vladimir

PY - 2020/7/1

Y1 - 2020/7/1

N2 - 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 L2 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.

AB - 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 L2 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.

KW - Approximations

KW - Kuznetsov

KW - KZK

KW - Non-linear acoustic

KW - NPE

KW - Westervelt equations

UR - http://www.scopus.com/inward/record.url?scp=85083497906&partnerID=8YFLogxK

U2 - 10.3934/dcds.2020179

DO - 10.3934/dcds.2020179

M3 - Article

AN - SCOPUS:85083497906

SN - 1078-0947

VL - 40

SP - 4231

EP - 4258

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 7

ER -

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

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