Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the quasilinear systems. The serve as important mathematical tools for modelling subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by study of behavioral economics. Different types were studied but left behind case and connections among them. This paper shows equivalence in solvability between associated systems, given their regular enough. Moreover, establish well-posedness results so do alone is interesting its own right from perspectives.