Geodesic
On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 175-188

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We study scalar conservation laws with power growth restriction on the flux vector. For such equations, we found correctness classes for the Cauchy problem among locally bounded generalized entropy solutions. These classes are determined by some exponents of admissible growth with respect to space variables. We give examples showing that enlargement of the growth exponent leads to failure of the correctness. 
@article{FPM_2006_12_5_a13,
     author = {E. Yu. Panov},
     title = {On well-posedness classes of locally bounded generalized entropy solutions of the {Cauchy} problem for quasilinear first-order equations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {175--188},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a13/}
}
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E. Yu. Panov. On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 175-188. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a13/