On the Cauchy problem for an integrable equation with peakon solutions

By Zhaoyang Yin. 2003

286 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fb7ba15810ccc0bd0de530ccb918bddb94d0140b

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

ON THE UNIQUENESS OF DISCONTINUOUS SOLUTIONS TO THE DEGASPERIS–PROCESI EQUATION (2007, methodology): “Regarding the well-posedness of the initial value problem for the DegasperisProcesi equation, Yin has studied this within certain functional classes in a series of papers [25, 26, 27, 28].”
On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, methodology): “[36] Given u0 ∈ Hs(R), s > 32 , there exist a maximal T = T (u0) > 0 and a unique solution u to Eq.”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, methodology): “The following result proved in [51] clarifies the relation between strong and weak solutions.”
Traveling wave solutions of the Degasperis-Procesi equation (2005, background): “3) have global solutions as well as smooth solutions that blow up in finite time (see [4–6,20,21]).”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, background): “For the DP equaltion we refer to [71], [72], [35] and [36].”
Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “The following result proved in [45] clarifies the relation between strong solutions and “strong” weak solutions.”
Stability of peakons for the Degasperis‐Procesi equation (2007, methodology): “We briefly collect the needed results from [24, 32, 33].”
Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, background): “1) may be chosen independently of s in the following sense [44].”
A note on the Cauchy problem of the Novikov equation (2013, background): “3) is that it not only has peakon solitons [17,18], i.”
On the well-posedness of the Degasperis-Procesi equation (2006, background): “In [37] he proved similar results for the Cauchy problem on R.”