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Well‐posedness, global existence, and blowup phenomena for a periodic quasi‐linear hyperbolic equation
Author(s) -
Constantin Adrian,
Escher Joachim
Publication year - 1998
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/(sici)1097-0312(199805)51:5<475::aid-cpa2>3.0.co;2-5
Subject(s) - uniqueness , gravitational singularity , mathematics , class (philosophy) , mathematical analysis , initial value problem , amplitude , physics , quantum mechanics , artificial intelligence , computer science
We establish the local well‐posedness of a recently derived model for small‐amplitude, shallow water waves. For a large class of initial data we prove global existence of the corresponding solution. Criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained, and an existence and uniqueness result for a class of global weak solutions is also given. © 1998 John Wiley & Sons, Inc.