Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system
This paper deals with the Cauchy problem for a system of conservation laws with a particular class of flux functions in \(m\) space dimensions. It is shown that initial data, with arbitrarily small total variations and uniformly close to a non-zero constant, such that the BV norm of admissible solution blows up instantaneously, no matter what criterion of admissibility is chosen among the ones proposed in the literature. In certain cases this occurs unless the system reduces to decoupled transport equations with constant coefficients. This work should be of interest to some one working on conservation laws.
scientific article; zbMATH DE number 2174753