Geodesic
On the connection of the Hamilton-Jacobi equation with some systems of quasilinear equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 206-219

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We show that the Hamilton-Jacobi equation with some conditions on the Hamiltonian can be associated with a quasilinear system of equations of the first order, which can be reduced to the vector Hopf equation. We find relations between the system of Riemann invariants and a specially constructed Hamilton-Jacobi equation. The result is illustrated with examples of a system of isentropic gas dynamics equations and a system of equations of chromatography. It is shown that the method of stochastic perturbations along characteristics allows to associate with the Hamilton-Jacobi equation a system of conservation laws.
Keywords: Hamilton-Jacobi equation, Hopf equation, system of Riemann invariants, viscous regularization, stochastic regularization. 
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     author = {O. S. Rozanova},
     title = {On the connection of the {Hamilton-Jacobi} equation with some systems of quasilinear equations},
     journal = {Trudy Instituta matematiki i mehaniki},
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O. S. Rozanova. On the connection of the Hamilton-Jacobi equation with some systems of quasilinear equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 206-219. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a17/