Sobolev space weak solutions to one kind of quasilinear parabolic partial differential equations related to forward-backward stochastic differential equations

This paper is concerned with the Sobolev type weak solutions of one class second order quasilinear parabolic partial differential equations (PDEs, for short). First all, similar to Feng, Wang and Zhao [9] Wu Yu [29], we use a family coupled forward-backward stochastic (FBSDEs, short) which satisfy monotonous assumption represent classical PDEs. Then, based on PDEs approximating PDEs, prove existence solutions. Moreover, principle norm equivalence employed link FBSDEs obtain uniqueness In summary, provide probabilistic interpretation enriches theory nonlinear