Abstract
Using probabilistic methods, we establish a priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity, which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward–backward stochastic differential equations.
Funding Statement
During the preparation of this work, the first author has been supported by the National Science Foundation under Grant No. DGE1610403 (2020–2023).
Acknowledgments
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
Citation
Joe Jackson. "On quasilinear parabolic systems and FBSDEs of quadratic growth." Ann. Appl. Probab. 34 (1A) 357 - 387, February 2024. https://doi.org/10.1214/23-AAP1966
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