Geodesic
An approximation scheme for measure-valued solutions of a first-order quasilinear equation
Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 87-113 
E. Yu. Panov. An approximation scheme for measure-valued solutions of a first-order quasilinear equation. Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 87-113. http://geodesic.mathdoc.fr/item/SM_1997_188_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A kinetic definition of a measure-valued solution of the Cauchy problem for a first-order quasilinear equation is presented. Using a suitable approximation of the right-hand side of the corresponding kinetic equation a family of equations is constructed. The unique solubility of Cauchy problems for these equations and the convergence (after possibly going over to a subsequence) of the resulting sequence of solutions to a generalized solution of the original problem are established.

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