Finite propagation speed for the Camassa-Holm equation

By Adrian Constantin. 2005

158 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6e14576e9d2707efa06778f3d0a414501420e177

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Yue Liu
2. Zhaoyang Yin
3. Zhiwu Lin
4. Lidiao Ni
5. Joachim Escher
6. Yong Zhou
7. David Henry
8. Lionel Rosier

In Statistical and Nonlinear Physics

1. Yue Liu
2. Zhaoyang Yin
3. Zhiwu Lin
4. Joachim Escher
5. David Henry
6. Yong Zhou
7. Lionel Rosier
8. Lidiao Ni

Citations in the corpus

• Stability of peakons for the Degasperis‐Procesi equation (2007, methodology): “Analogous to the case of Camassa-Holm equation [6], Henry [19] and Mustafa [29] showed that smooth solutions to equation (1.”
• Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, methodology): “Analogous to the case of Camassa-Holm equation [ 8 ], Henry [27] and Mustafa [41] showed that smooth solutions to Eq. (1.2) have infinite speed of propagation.”
• Compactly Supported Solutions of the Camassa-Holm Equation (2005, methodology): “Our approach is also simpler than the one pursued in [ 4 ].”
• A new asymptotic behavior of solutions to the Camassa-Holm equation (2012, background): “In a recent work [2], it was shown that u cannot preserve compact support in a non-trivial time interval except u ≡ 0.”
• Blow-up of solutions to the DGH equation (2007, background): “Recently, in [22], among others, Himonas, Misiołek, Ponce and the author showed the infinite propagation speed for the Camassa–Holm equation in the sense that a strong solution of the Cauchy problem with compact initial profile cannot be compactly supported at any later time unless it is the zero so”
• A Note on the Degasperis-Procesi Equation (2005, unknown): “We will prove that the infinite propagation speed of smooth solutions, observed in [11] for the Camassa-Holm equation, is also a feature of the model (1.”
• On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, methodology): “Analogous to the case of Camassa-Holm equation [9], Henry [24] showed that smooth solutions to Eq.”
• Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, result): “Analogous to the case of Camassa–Holm equation [9], Henry [26] and Mustafa [42] showed that smooth solutions to Eq.”
• Infinite propagation speed for a two component Camassa-Holm equation (2009, result): “These results have analogues in the case where � ≡ 0, which is simply the CH equation [ 10 , 30, 32].”
• Unique continuation property and control for the Benjamin–Bona–Mahony equation on a periodic domain (2013, methodology): “We point out that a moment approach, inspired by the paper [7] that was concerned with the UCP for the Camassa–Holm equation (see also [14]), was nevertheless applied in [29] to prove the UCP for the Kadomtsev–Petviashvili (KP)–BBM-II equation.”