Cohen, Amy; Kappeler, Thomas (1987). Solutions to the Korteweg–de Vries Equation with Initial Profile in $L_1^1 (\mathbb{R}) \cap L_N^1 (\mathbb{R}^ + )$. SIAM Journal on Mathematical Analysis, 18(4):991-1025.
The Cauchy problem for the Korteweg–de Vries equation is considered with initial profile integrable against $(1 + | x |)dx$ on $\mathbb{R}$ and against $(1 + | x |)^N dx$ on $\mathbb{R}^ + $. Classical solutions are constructed for $N \geqq {{11} / 4}$. Under mild additional hypotheses the solution evolves in $L^2 (\mathbb{R})$.
The Cauchy problem for the Korteweg–de Vries equation is considered with initial profile integrable against $(1 + | x |)dx$ on $\mathbb{R}$ and against $(1 + | x |)^N dx$ on $\mathbb{R}^ + $. Classical solutions are constructed for $N \geqq {{11} / 4}$. Under mild additional hypotheses the solution evolves in $L^2 (\mathbb{R})$.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Language: | English |
| Date: | 1987 |
| Deposited On: | 20 Oct 2009 14:36 |
| Last Modified: | 23 Mar 2022 14:55 |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 0036-1410 |
| Additional Information: | Copyright © 1987, Society for Industrial and Applied Mathematics |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1137/0518076 |
| Related URLs: | http://portal.acm.org/citation.cfm?id=35885 |
Cohen, Amy