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October  2009, 12(3): 657-670. doi: 10.3934/dcdsb.2009.12.657

Blow up and propagation speed of solutions to the DGH equation

Yong Zhou 1, and  Zhengguang Guo 1,

1. 

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China, China

Received  December 2008 Revised  May 2009 Published  July 2009

A wave-breaking mechanism for solutions with certain initial profiles and propagation speed are discussed in this paper. Firstly, we apply the best constant to give sufficient condition via an appropriate integral form of the initial data, which guarantees finite time singularity formation for the corresponding solution, then we establish blow up criteria via the conserved quantities. Finally, persistence properties of the strong solutions are presented and infinite propagation speed is also investigated in the sense that the corresponding solution $u(x,t)$ does not have compact spatial support for $t>0$ though $u_0 \in C_0^{\infty}(\mathbb{R})$.
Keywords: Best constant, Propagation speed., Integrable equation, Singularity.
Mathematics Subject Classification: 30C70, 37L05, 35Q58, 58E3.
Citation: Yong Zhou, Zhengguang Guo. Blow up and propagation speed of solutions to the DGH equation. Discrete and Continuous Dynamical Systems - B, 2009, 12 (3) : 657-670. doi: 10.3934/dcdsb.2009.12.657
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