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.
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