Controllability of the moments for Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation

Preprint English OPEN
Rozanova-Pierrat , Anna;
(2006)
  • Publisher: HAL CCSD
  • Subject: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC] | [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]

Recalling the proprieties of the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation, we prove the controllability of moments result for the linear part of KZK equation. Then we prove the local controllability result for the full KZK equation applying a known method of pertur... View more
  • References (34)
    34 references, page 1 of 4

    [1] S.I. Aanonsen et al. Distortion and harmonic generation in the nearfield of finite amplitude sound beam. J. Acoust. Soc. Am., vol. 75, No. 3, 1984, p. 749-768.

    [2] S.Alinhac A minicourse on global existence and blowup of classical solutions to multidimensional quasilinear wave equations. Journ´ees E´quations aux d´eriv´ees partielles, Forges-les-Eaux, 3-7 juin 2002.

    [3] S. Alinhac Explosion des solutions d'une ´equation d'ondes quasi-lin´eaire en deux dimensions d'espace. Comm. PDE 21 (5,6), 1996, p.923-969.

    [4] S. Alinhac Blowup for nonlinear hyperbolic equations, Progress in Nonlinear Differential Equations and their Applications, Birkh¨auser, Boston, 1995.

    [5] S. Alinhac Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions, II. Acta Math., 182 (1999), 1-23.

    [6] S. Alinhac Blowup of small data solutions for a quasilinear wave equation in two space dimensions, Annals of Math., 149 (1999), 97-127.

    [7] S. Alinhac, P. G´erard Op´erateurs pseudo-differentiels et th´eor`eme de Nash-Moser. InterEditions, Paris, 1991.

    [8] M.A. Averkiou, Y.-S. Lee, M.F. Hamilton Self-demodulation of amplitudeand frequency-modulated pulses in a thermoviscous fluid. J. Acoust. Soc. Am. 94 (5), 1993, p. 2876-2883.

    [9] M.A. Averkiou, M.F. Hamilton Nonlinear distortion of short pulses radiated by plane and focused circular pistons. J. Acoust. Soc. Am. 102 (5), Pt.1, 1997, p. 2539-2548.

    [10] N.S. Bakhvalov, Ya. M. Zhileikin and E.A. Zabolotskaya Nonlinear Theory of Sound Beams, American Institute of Physics, New York, 1987 ( Nelineinaya teoriya zvukovih puchkov, Moscow “Nauka”, 1982).

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