On the zero‐dispersion limit of the benjamin‐ono cauchy problem for positive initial data | Zendy

Miller Peter D. | Zendy; Xu Zhengjie | Zendy

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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.

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