Abstract:
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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