In this paper, we study systems of conservation laws in one space dimension. We prove that for classical solutions in Sobolev spaces Hs, 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.
John M. Holmes, Barbara Lee Keyfitz
. Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws[J]. Communications on Applied Mathematics and Computation, 2024
, 6(1)
: 489
-500
.
DOI: 10.1007/s42967-023-00267-9
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