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The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-29
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
A nonlinear partial differential equation containing the famous Camassa-Holm and Degasperis-Procesi equations as special cases is investigated.
The Kato theorem for abstract differential equations is applied to establish the local well-posedness of solutions for the equation in the Sobolev space Hs(R) with s>3/2.
Although the H1-norm of the solutions to the nonlinear model does not remain constant, the existence of its weak solutions in the lower-order Sobolev space Hs with 1≤s≤3/2 is proved under the assumptions u0∈Hs and ∥u0x∥L∞<∞.
American Psychological Association (APA)
Lai, Shaoyong& Wang, Aiyin. 2012. The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-505090
Modern Language Association (MLA)
Lai, Shaoyong& Wang, Aiyin. The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation. Abstract and Applied Analysis No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-505090
American Medical Association (AMA)
Lai, Shaoyong& Wang, Aiyin. The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-505090
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505090