Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics
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چکیده
The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution u = u(t, x), an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities u and v = 2 arctanux along each characteristic, it is proved that the Cauchy problem with general initial data u0 ∈ H(IR) has a unique solution, globally in time.
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تاریخ انتشار 2014