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Parabolic Schemes for Quasi-Linear Parabolic and Hyperbolic PDEs via Stochastic Calculus
We consider two quasi-linear initial-value Cauchy problems on ℝ d : a parabolic system and an hyperbolic one. They both have a first order non-linearity of the form φ(t, x, u)·∇u, a forcing term h(t, x, u) and an initial condition u 0 ∈ L ∞(ℝ d ) ∩ C …