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期刊论文
Initial Boundary Value Problems of the Camassa-Holm Equation
Communications in Partial Differential Equations, 33: 377-395, 2008,-0001,():
In this paper we study initial boundary value problems of the Camassa-Holm equation on the half line and on a compact interval. Using rigorously the conservation of symmetry, it is possible to convert these boundary value problems into Cauchy problems for the Camassa-Holm equation on the line and on the circle, respectively. Applying thus known results for the latter equations we first obtain the local well-posedness of the initial boundary value problems under consideration. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions for the equation on the half line and on a compact interval, respectively. An interesting result of our analysis shows that the Camassa-Holm equation on a compact interval possesses no nontrivial global classical solutions.
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