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2008 | 81 | 1 | 157-174
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Initial boundary value problems of the Degasperis-Procesi equation

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We mainly study initial boundary value problems for the Degasperis-Procesi equation on the half line and on a compact interval. By the symmetry of the equation, we can convert these boundary value problems into Cauchy problems on the line and on the circle, respectively. Applying thus known results for the equation on the line and on the circle, we first obtain the local well-posedness of the initial boundary value problems. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions on the half line and on a compact interval, respectively. One interesting result is that the corresponding strong solution to the Degasperis-Procesi equation on the half line blows up in finite time provided the initial potential, assumed nonpositive, is not identically zero. Another one is that all global strong solutions to the Degasperis-Procesi equation on a compact interval blow up in finite time.
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Twórcy
  • Institute for Applied Mathematics, Leibniz University of Hannover, D-30167 Hannover, Germany
autor
  • Department of Mathematics, Zhongshan University, 510275 Guangzhou, China
  • Institute for Applied Mathematics, Leibniz University of Hannover, D-30167 Hannover, Germany
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-10
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