TY - RPRT
T1 - An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation
Y1 - 2005
A1 - Alberto Bressan
A1 - Massimo Fonte
AB - In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.
JF - Methods Appl. Anal. 12 (2005) 191-219
UR - http://hdl.handle.net/1963/1719
U1 - 2432
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -