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Mat. Sb., 2019, Volume 210, Number 5, Pages 72–108 (Mi msb8978)  

This article is cited in 2 scientific papers (total in 2 papers)

Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation

P. I. Naumkin

Center of Mathematical Sciences, National Autonomous University of Mexico, Morelia, Mexico

Abstract: The large-time behaviour of solutions of the Cauchy problem for the modified Kawahara equation
$$ \begin{cases} u_t-\partial_xu^3-\frac a3\partial_x^3u+\frac b5\partial_x^5u=0,&(t,x)\in\mathbb R^2,
u(0,x)=u_0(x),&x\in\mathbb R, \end{cases} $$
where $a,b>0$, is investigated. Under the assumptions that the total mass of the initial data $\int u_0(x) dx$ is nonzero and the initial data $u_0$ are small in the norm of $\mathbf H^{2,1}$ it is proved that a global-in-time solution exists and estimates for its large-time decay are found.
Bibliography: 19 titles.

Keywords: Kawahara equation, cubic nonlinearity, large-time asymptotics.

Funding Agency Grant Number
CONACYT - Consejo Nacional de Ciencia y Tecnología CB16RF283698
Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica IN100616
This research was carried out with the support of Consejo Nacional de Ciencia y Tecnología – CONACYT (project no. CB16RF283698) and Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica – PAPIIT (project no. IN100616).


DOI: https://doi.org/10.4213/sm8978

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English version:
Sbornik: Mathematics, 2019, 210:5, 693–730

Bibliographic databases:

UDC: 517.956.8+517.953
MSC: 35B40, 35Q53
Received: 12.06.2017 and 18.01.2019

Citation: P. I. Naumkin, “Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation”, Mat. Sb., 210:5 (2019), 72–108; Sb. Math., 210:5 (2019), 693–730

Citation in format AMSBIB
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\jour Sb. Math.
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\pages 693--730
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Faminskii, E. V. Martynov, “O nachalno-kraevoi zadache na poluosi dlya obobschennogo uravneniya Kavakhary”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 683–699  mathnet  crossref
    2. Naumkin P.I., Perez J.J., “Modified Kdv Equation With Higher Order Dispersion Terms”, NoDea-Nonlinear Differ. Equ. Appl., 27:1 (2020), 1  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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