ON THE UNIQUENESS OF DISCONTINUOUS SOLUTIONS TO THE DEGASPERIS–PROCESI EQUATION
ON THE UNIQUENESS OF DISCONTINUOUS SOLUTIONS TO THE DEGASPERIS–PROCESI EQUATION
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DOI：
10.1016/j.jde.2006.11.008
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发表时间：
2007-03
影响因子：
2.4
通讯作者：
G. Coclite;K. Karlsen
中科院分区：
文献类型：
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作者：
G. Coclite;K. Karlsen
We prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive Degasperis–Procesi equation In a recent paper [G.M. Coclite, K.H. Karlsen, On the well-posedness of the Degasperis–Procesi equation, J. Funct. Anal. 233 (2006) 60–91], we proved for this equation the existence and uniqueness of L1∩BV weak solutions satisfying an infinite family of Kružkov-type entropy inequalities. The purpose of this paper is to replace the Kružkov-type entropy inequalities by an Oleĭnik-type estimate and to prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Degasperis–Procesi equation is admissible only if it jumps down in value (like the inviscid Burgers equation).
