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On a quasilinear nonlocal Benney system
Abstract
We study a quasilinear nonlocal Benney system and establish the existence and uniqueness of strong local in time solutions to the corresponding Cauchy problem. We also show, under certain conditions, the blow-up of such solutions in finite time. Furthermore, we prove the existence of global weak solutions and exhibit bound-state solutions to this system.
Communicated by F. Bouchut
AMSC: 35L03, 35Q55, 35Q70
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Published: 16 March 2017
