Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion - Escher, Joachim; Li, Baihong; Wei, Yuanhong (Nonlinear differential equations and applications, 2025)
This paper investigates the Cauchy problem associated with the Degasperis-Procesi equation modified by weak dissipation and linear dispersion. Besides well-posedness of the Cauchy problem, our focus is on exploring two critical aspects: describing conditions which imply global existence versus wave breaking phenomena of solutions. We provide sufficient conditions that guarantee global existence of solutions when both dissipation and dispersion effects are present. We also highlight the impact of the dissipativity and dispersion parameter on the qualitative behaviour of solutions such as wave breaking, presenting new insights into the dynamics of the modified Degasperis-Procesi equation.