Global weak solutions and wave breaking phenomena to the periodic Degasperis-Procesi equation with strong dispersion
The author considers the initial value problem for the periodic Degasperis-Procesi equation with one spatial dimension. The DP-equation is a third-order dispersive conservation law. The dispersive term is assumed to be strong. Such problems appear as an approximation to the incompressible Euler equation for shallow water waves. The existence and uniqueness of the global weak solution are established. Periodic peakon and shock-peakon solutions are constructed. Moreover, two conservation laws (i.e. first integrals) are revealed.
scientific article; zbMATH DE number 5612956
scientific article