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• W3213955059 startingPage "110828" @default.
• W3213955059 abstract "We propose a globally convergent numerical method, called the convexification, to numerically compute the viscosity solution to first-order Hamilton-Jacobi equations through the vanishing viscosity process where the viscosity parameter is a fixed small number. By convexification, we mean that we employ a suitable Carleman weight function to convexify the cost functional defined directly from the form of the Hamilton-Jacobi equation under consideration. The strict convexity of this functional is rigorously proved using a new Carleman estimate. We also prove that the unique minimizer of the this strictly convex functional can be reached by the gradient descent method. Moreover, we show that the minimizer well approximates the viscosity solution of the Hamilton-Jacobi equation as the noise contained in the boundary data tends to zero. Some interesting numerical illustrations are presented." @default.
• W3213955059 created "2021-11-22" @default.
• W3213955059 creator A5000863257 @default.
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• W3213955059 date "2022-02-01" @default.
• W3213955059 modified "2023-10-18" @default.
• W3213955059 title "Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method" @default.
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• W3213955059 doi "https://doi.org/10.1016/j.jcp.2021.110828" @default.
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