Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation
By Yue Liu, Zhaoyang Yin. 2006
352 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cb7d204b4e974505405af8a90968a1f22fc1a567
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In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “Recently, several new global existence and blow-up results for strong solutions to the Degasperis-Procesi equation on the line were presented in [34].”
- Inverse scattering transform for the Degasperis–Procesi equation (2010, background): “1) is ensured at any later time t > 0 (see [14, 31, 43]).”
- Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, methodology): “Wave breaking phenomena and global existence of solutions of the Degasperis-Procesi equation were investigated in [8,26,43], for example.”
- On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, methodology): “[29] Assume u0 ∈ Hs(R), s > 32 and there exists x0 ∈ R such that { y0(x) ≤ 0 if x ≤ x0, y0(x) ≥ 0 if x ≥ x0.”
- Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, methodology): “Wave breaking phenomena and global existence of solutions for the Degasperis–Procesi equation were investigated in [6,16,18,19,34,35].”
- Stability of peakons for the Degasperis‐Procesi equation (2007, background): “Under the assumption y0 = u0 − ∂(2) xu0 ≥ 0 in Theorem 1, the existence is global in time [24], that is T = +∞.”
- On the blow-up of solutions to the integrable modified Camassa–Holm equation (2014, result): “It is shown that even when the initial momentum density m0(x) does not change sign, the solutions to the Cauchy problem (1.1) may blow up in finite time, in contrast to the CH equation, the Degasperis–Procesi (DP) equation [10, 18], or the Novikov equation (1.5).”
- Analysis on the blow-up of solutions to a class of integrable peakon equations (2016, methodology): “2) and we have used the following estimate (see [23]) 1 4 ‖u(t)‖(2)2 = 1 4 ∫”