On the Burgers–Poisson equation
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Original versionJournal of Differential Equations. 2016, 261 (6), 3220-3246. 10.1016/j.jde.2016.05.028
In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 (R). In addition an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.