The Camassa-Holm equation --- a survey
Helge Holden ,
(Norwegian University of Science and Technology)
Jueves 31 de enero 2013
abstract: The Camassa-Holm equation u_t-u_{xxt}+ u_x+3u u_x-2u_x
u_{xx}-u u_{xxx}=0 has received considerable attention the last 20
years due to its many intriguing mathematical properties. In
particular, the Cauchy problem possesses two distinct classes of
solutions due to the wave breaking of the solution. We review the
current understanding of this problem, with emphasis on the Lipschitz
stability of the solution of the Cauchy problem. Extensions to a
two-component generalization of the Camassa-Holm equation will also be
discussed. The talk is based on joint work with X. Raynaud (University
of Oslo) and K. Grunert (Norwegian University of Science and
Technology).