Article ID Journal Published Year Pages File Type
5775004 Journal of Mathematical Analysis and Applications 2017 36 Pages PDF
Abstract
In this study, we consider the Cauchy problem for the second-order Camassa-Holm equation with periodic initial data u0. Using the vanishing viscosity method, the local weak solution of the equation is obtained in the finite energy space. A continuous semigroup of weak conservative solutions in Lagrangian coordinates is constructed. In particular, for any two solutions u(t) and v(t) of the equation, a Lipschitz metric dD is constructed with the property that dD(u(t),v(t))≤eCtdD(u0,v0).
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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