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math.AP2022★ 3 cited
Hamilton-Jacobi equations with monotone nonlinearities on convex cones
Hong-Bin Chen, Jiaming Xia
We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no…
math.AP2022★ 2 cited
Hamilton-Jacobi equations from mean-field spin glasses
Hong-Bin Chen, Jiaming Xia
We give a meaning to the Hamilton--Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defi…