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arXiv · 2206.08334

On quasilinear parabolic systems and FBSDEs of quadratic growth

Joe Jackson
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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.

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Joe Jackson. 2022-06-16. On quasilinear parabolic systems and FBSDEs of quadratic growth. https://arxiv.org/abs/2206.08334

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