Global weak solutions for a new periodic integrable equation with peakon solutions

By Zhaoyang Yin. 2004

213 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1e16d35929ba3b9835318de15b88cdee84e8d534

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, background): “The global existence of strong solutions and global weak solutions and blow-up structure to Eq.(1.2) were investigated in [ 38 , 39].”
Global weak solutions for the Novikov equation (2011, background): “solutions of the form u(t, x) = c e−|x−ct | and periodic peakon solutions [29], but also shock peakons [4, 20] which are given by u(t, x) = − 1 t + k sgn(x) e−|x|, k > 0, and periodic shock peakons [15].”
Well-posedness and global existence for the Novikov equation (2012, background): “at the form u(t, x) = ce−|x−ct | and periodic peakon solutions [23], but also shock peakons [5, 18] which are given by”
On the well-posedness of the Degasperis-Procesi equation (2006, result): “Similar results for the periodic case can be found in [39].”
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].”
A Note on the Degasperis-Procesi Equation (2005, background): “1) in H(R), with s > 3 2 can be established provided the initial data is in H(R) (see [23]), and finite-time blowup is possible only if the slope of the solution becomes unbounded in finite time [22].”
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “The global existence of strong solutions and global weak solutions to Eq. (1.2) are also investigated in [ 49 , 50].”