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Analyticity and smoothing effect for the Korteweg de Vries equation with a single point singularity

✍ Scribed by Keiichi Kato; Takayoshi Ogawa

Publisher: Springer
Year: 2000
Tongue: English
Weight: 208 KB
Volume: 316
Category: Article
ISSN: 0025-5831
DOI: 10.1007/s002080050345

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## Abstract The aim of this work is to consider the Korteweg–de Vries equation in a finite interval with a very weak localized dissipation namely the __H__^−1^‐norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the