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Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation. (English) Zbl 1213.35133
Holden, Helge (ed.) et al., Nonlinear partial differential equations and hyperbolic wave phenomena. The 2008--2009 research program on nonlinear partial differential equations, Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4976-7/pbk). Contemporary Mathematics 526, 199-220 (2010).
Summary: We first establish the local well-posedness for a modified two-component Camassa-Holm equation by Kato’s semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the equation. Finally, we present two blow-up results for strong solutions to the equation. For the entire collection see [Zbl 1200.35002].

35B44Blow-up (PDE)
35G25Initial value problems for nonlinear higher-order PDE
47D06One-parameter semigroups and linear evolution equations