Title Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system. Publication Type Journal Article Year of Publication 2005 Authors De Lellis C. Journal Duke Mathematical Journal Volume 127 Pagination 313–339 Publisher Duke University Press Type of Article hyperbolic conservation laws ISSN 0012-7094 Abstract We consider the Cauchy problem for the system ?tui + divz(g(\ensuremath|u\ensuremath|)ui) = 0, i ? {1,?, k}, in m space dimensions and with g ? C3. When k ? 2 and m = 2, we show a wide choice of g's for which the bounded variation (BV) norm of admissible solutions can blow up, even when the initial data have arbitrarily small oscillation and arbitrarily small total variation, and are bounded away from the origin. When m ? 3, we show that this occurs whenever g is not constant, that is, unless the system reduces to k decoupled transport equations with constant coefficients. Notes Duke Math. J. 127 (2005), no. 2, 313–339. URL https://projecteuclid.org/euclid.dmj/1111609854 DOI 10.1215/S0012-7094-04-12724-1
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