Abstract:
Measure-valued solutions of the Cauchy problem are considered for a first-order quasilinear equation with only continuous flow functions. A measure-valued analogue of the maximum principle (in Lebesgue spaces) is proved. Conditions are found under which a measure-valued solution is an ordinary function. Uniqueness questions are studied. The class of “strong” measure-valued solutions is distinguished and the existence and uniqueness (under natural restrictions) of a strong measure-valued solution is proved. Questions of the convergence of sequences of measure-valued solutions are studied.
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