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This article is cited in 6 scientific papers (total in 6 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.
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
Linking options:
https://www.mathnet.ru/eng/sm8978https://doi.org/10.1070/SM8978 https://www.mathnet.ru/eng/sm/v210/i5/p72
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Abstract page: | 281 | Russian version PDF: | 24 | English version PDF: | 7 | References: | 22 | First page: | 8 |
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