Stability to a Generalized Degasperis-Procesi Equation

Abstract

A nonlinear generalized Degasperis-Procesi equation is investigated. Assuming that the strong solution of the equation is bounded in the sense of L ∞ (R)-norm and the initial data belong to the space L 1 (R) ∩ L 2 (R), we prove that the solutions are stable in the space L 1 (R)