Geodesic
Multidimensional scalar conservation laws
Sbornik. Mathematics, Tome 194 (2003) no. 1, pp. 151-164
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A new approach, based on a priori estimates, to the demonstration of the occurrence of a gradient catastrophe of solutions of multidimensional scalar conservation laws is considered. Upper estimates for the time of the gradient catastrophe are derived. A counterexample is presented showing that the estimate so obtained is asymptotically best possible in the general class of problems under consideration. 
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S. I. Pokhozhaev. Multidimensional scalar conservation laws. Sbornik. Mathematics, Tome 194 (2003) no. 1, pp. 151-164. http://geodesic.mathdoc.fr/item/SM_2003_194_1_a7/

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