The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation
Abstract
We consider a three-parameter family of non-linear equations with (p+1)-order non-linearities. Such family includes as a particular member the well-known b-equation, which encloses the famous Camassa-Holm equation. For certain choices of the parameters we establish a global existence result and show a scenario that prevent the wave breaking of solutions. Also, we explore unique continuation properties for some values of the parameters.
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