arXiv:2206.08334 Abstract | arXiv Analytics

arXiv:2206.08334 [math.PR]Abstract References Reviews Resources

On quasilinear parabolic systems and FBSDEs of quadratic growth

Published 2022-06-16Version 1

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.

Categories: math.PR, math.AP

Subjects: 60H30

Keywords: quasilinear parabolic systems, quadratic growth, forward-backward stochastic differential equations, partial differential equations, establish a-priori estimates

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