Initial boundary value problems of the Degasperis-Procesi equation

Tom 81 / 2008

Joachim Escher, Zhaoyang Yin Banach Center Publications 81 (2008), 157-174 MSC: 35G25, 35L05. DOI: 10.4064/bc81-0-10

Streszczenie

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.

Autorzy

  • Joachim EscherInstitute for Applied Mathematics
    Leibniz University of Hannover
    D-30167 Hannover, Germany
    e-mail
  • Zhaoyang YinDepartment of Mathematics
    Zhongshan University
    510275 Guangzhou, China
    and
    Institute for Applied Mathematics
    Leibniz University of Hannover
    D-30167 Hannover, Germany
    e-mail

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