Geodesic
On measure-valued solutions of the Cauchy problem for a~first-order quasilinear equation
Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 335-377

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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. 
@article{IM2_1996_60_2_a4,
     author = {E. Yu. Panov},
     title = {On measure-valued solutions of the {Cauchy} problem for a~first-order quasilinear equation},
     journal = {Izvestiya. Mathematics },
     pages = {335--377},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a4/}
}
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E. Yu. Panov. On measure-valued solutions of the Cauchy problem for a~first-order quasilinear equation. Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 335-377. http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a4/