Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

doi:10.1007/s42967-023-00267-9

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 489-500.doi: 10.1007/s42967-023-00267-9

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Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

John M. Holmes, Barbara Lee Keyfitz

Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

收稿日期:2022-12-21 修回日期:2022-12-21 发布日期:2024-04-16
通讯作者: Barbara Lee Keyfitz,E-mail:keyfitz.2@osu.edu;John M. Holmes,E-mail:holmes.782@osu.edu E-mail:keyfitz.2@osu.edu;holmes.782@osu.edu
基金资助:
The first author was supported in part by the NSF Grant DMS-2247019.

Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

John M. Holmes, Barbara Lee Keyfitz

Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

Received:2022-12-21 Revised:2022-12-21 Published:2024-04-16
Contact: Barbara Lee Keyfitz,E-mail:keyfitz.2@osu.edu;John M. Holmes,E-mail:holmes.782@osu.edu E-mail:keyfitz.2@osu.edu;holmes.782@osu.edu
Supported by:
The first author was supported in part by the NSF Grant DMS-2247019.

摘要/Abstract

摘要： 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.

关键词: Conservation laws, Data-to-solution map, Nonuniform dependence

Abstract: 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.

Key words: Conservation laws, Data-to-solution map, Nonuniform dependence

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.

参考文献

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Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

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