Dynamical Properties of Solutions for Various Types of Nonlinear Partial Differential Equations - Li, Rui (Curtin University, 2019)
In this thesis, we investigate the existence of global weak solutions for a generalized Benjamin-Bona-Burgers equation and a nonlinear equation with quartic nonlinearities. The existence of local weak solutions and well-posedness of local strong solutions are established for two nonlinear equations with quadratic and cubic nonlinearities, respectively. Moreover, conditions of wave breaking for a generalized Degasperis-Procesi equation are obtained.