Cauchy problems for fifth-order KdV equations in weighted Sobolev spaces
In this work we study the initial-value problem for the fifth-order Korteweg-de Vries equation $$ \partial_{t}u+\partial_{x}^{5}u+u^k\partial_{x}u=0, \quad x,t\in \mathbb{R}, \; k=1,2, $$ in weighted Sobolev spaces $H^s(\mathbb{R})\cap L^2(\langle x \rangle^{2r}dx)$. We prove local and glob...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/141/abstr.html |
| Summary: | In this work we study the initial-value problem for the fifth-order
Korteweg-de Vries equation
$$
\partial_{t}u+\partial_{x}^{5}u+u^k\partial_{x}u=0,
\quad x,t\in \mathbb{R}, \; k=1,2,
$$
in weighted Sobolev spaces $H^s(\mathbb{R})\cap L^2(\langle x \rangle^{2r}dx)$.
We prove local and global results. For the case $k=2$ we point out the
relationship between decay and regularity of solutions of the
initial-value problem. |
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| ISSN: | 1072-6691 |