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

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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 1987 20 Oct 2009 14:33 05 Apr 2016 13:29 Society for Industrial and Applied Mathematics (SIAM) 0895-4798 https://doi.org/10.1137/0518076
Permanent URL: https://doi.org/10.5167/uzh-22987