Initial boundary value problems of the Degasperis-Procesi equation

Joachim Escher, and Zhaoyang Yin. "Initial boundary value problems of the Degasperis-Procesi equation." Banach Center Publications 81.1 (2008): 157-174. <http://eudml.org/doc/281636>.

@article{JoachimEscher2008,
abstract = {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.},
author = {Joachim Escher, Zhaoyang Yin},
journal = {Banach Center Publications},
keywords = {local well-posedness; blow-up and global existence; global and local weak solutions; half line; compact interval},
language = {eng},
number = {1},
pages = {157-174},
title = {Initial boundary value problems of the Degasperis-Procesi equation},
url = {http://eudml.org/doc/281636},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Joachim Escher
AU - Zhaoyang Yin
TI - Initial boundary value problems of the Degasperis-Procesi equation
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 157
EP - 174
AB - 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.
LA - eng
KW - local well-posedness; blow-up and global existence; global and local weak solutions; half line; compact interval
UR - http://eudml.org/doc/281636
ER -