The Nonconvex Multi-Dimensional Riemann Problem for Hamilton-Jacobi Equations

Abstract

Simple inequalities are presented for the Riemann problem for a Hamilton Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities whereever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained. Keywords: Hamilton Jacobi equations; Riemann problem; Godunov scheme.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1989
Accession Number
ADA212619

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  • Stanley Osher

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