We propose a new splitting algorithm to solve a class of semilinear parabolic PDEs with convex and quadratic growth gradients. By splitting the original equation into a linear parabolic equation and a Hamilton-Jacobi equation, we are able to solve both equations explicitly. In particular, we solve the associated Hamilton-Jacobi equation by the Hopf-Lax formula, and interpret the splitting algorithm as a Hopf-Lax splitting approximation of the semilinear parabolic PDE. We prove that the solution of the splitting scheme will converge to the viscosity solution of the equation, obtaining its convergence rate via Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation.
Joint work with Shuo Huang and Thaleia Zariphopoulou. 

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