Email this article Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation
- Authors: Naumkin P.I.1
-
Affiliations:
- National Autonomous University of Mexico, Center of Mathematical Sciences
- Issue: Vol 210, No 5 (2019)
- Pages: 72-108
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133273
- DOI: https://doi.org/10.4213/sm8978
- ID: 133273
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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.
About the authors
Pavel Ivanovich Naumkin
National Autonomous University of Mexico, Center of Mathematical Sciences
Email: pavelni@matmor.unam.mx
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