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arXiv · 2201.01137

Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems

Qian Lei·Chi Seng Pun
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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.

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Qian Lei, Chi Seng Pun. 2022-01-04. Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems. https://arxiv.org/abs/2201.01137

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