Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems
Abstract
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling the subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by the study of behavioral economics. Different types of nonlocal parabolic systems were studied but left behind the fully-nonlinear case and the connections among them. This paper shows the equivalence in solvability between nonlocal fully-nonlinear and the associated quasilinear systems, given their solutions are regular enough. Moreover, we establish the well-posedness results for the nonlocal quasilinear parabolic systems, so do that for the nonlocal fully-nonlinear parabolic systems. The quasilinear case alone is interesting in its own right from mathematical and modelling perspectives.
Cite
@article{arxiv.2201.01137,
title = {Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems},
author = {Qian Lei and Chi Seng Pun},
journal= {arXiv preprint arXiv:2201.01137},
year = {2022}
}