Blow up and propagation speed of solutions to the DGH equation
Blow up and propagation speed of solutions to the DGH equation
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DOI：
10.3934/dcdsb.2009.12.657
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发表时间：
2009-07
影响因子：
1.2
通讯作者：
Yong Zhou;Zhengguang Guo
中科院分区：
文献类型：
--
作者：
Yong Zhou;Zhengguang Guo
本文讨论了具有一定初始剖面和传播速度的解的破波机理。首先，我们应用最佳常数通过初值的适当积分形式给出充分条件，从而保证相应解在有限时间内形成奇性，然后通过守恒量建立爆破准则。最后，给出了强解的持久性，并在相应的解$u(x，t)$在C0^{INFTY}(\mathbb{R})$中不具有对$t>；0$到$u_0的紧空间支撑性的意义下研究了无穷传播速度.
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 $u_0 \in C_0^{\infty}(\mathbb{R})$.