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Solutions to the Korteweg–de Vries Equation with Initial Profile in $L_1^1 (\mathbb{R}) \cap L_N^1 (\mathbb{R}^ + )$


Cohen, A (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 Matrix Analysis and Applications, 18:991-1025.

Abstract

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 $L^2 (\mathbb{R})$.

Abstract

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 $L^2 (\mathbb{R})$.

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Additional indexing

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 14:33
Last Modified:05 Apr 2016 13:29
Publisher:Society for Industrial and Applied Mathematics (SIAM)
ISSN:0895-4798
Publisher DOI:https://doi.org/10.1137/0518076

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