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.
|35G25||Initial value problems for nonlinear higher-order PDE|
|47D06||One-parameter semigroups and linear evolution equations|