Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws
John M. Holmes , Barbara Lee Keyfitz
Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1) : 489 -500.
In this paper, we study systems of conservation laws in one space dimension. We prove that for classical solutions in Sobolev spaces $H^s$, with s > 3/2, the data-to-solution map is not uniformly continuous. Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.
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