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On the zero‐dispersion limit of the benjamin‐ono cauchy problem for positive initial data
Author(s) -
Miller Peter D.,
Xu Zhengjie
Publication year - 2011
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20345
Subject(s) - limit (mathematics) , mathematics , zero (linguistics) , initial value problem , cauchy distribution , dispersion (optics) , cauchy problem , mathematical analysis , mathematical physics , physics , quantum mechanics , philosophy , linguistics
We study the Cauchy initial‐value problem for the Benjamin‐Ono equation in the zero‐dispersion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg–de Vries equation. © 2010 Wiley Periodicals, Inc.