On convergence to entropy solutions of a single conservation law

B. Cockburn; G. Gripenberg; S. O. Londen

doi:10.1006/jdeq.1996.0094

On convergence to entropy solutions of a single conservation law

B. Cockburn
, G. Gripenberg
, S. O. Londen

School of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Estimates of the difference between the entropy solutions of the single conservation law u_t+div g(u) = 0, u(0, ·) = u₀ and of the evolutionary integral equation (k * (u-u₀))_t+div g(u) = 0 are given in terms of k, g and u₀. A corresponding result is obtained for more general evolution equations with an accretive non-linearity.

Original language	English (US)
Pages (from-to)	206-251
Number of pages	46
Journal	Journal of Differential Equations
Volume	128
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1996.0094
State	Published - Jun 10 1996

Bibliographical note

Funding Information:
* Partially supported by NSF Grant DMS-94-07952. E-mail: cockburn -E-mail: Gustaf.Gripenberg helsinki.fi. E-mail: Stig-Olof.Londen hut.fi.

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10.1006/jdeq.1996.0094

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abstract = "Estimates of the difference between the entropy solutions of the single conservation law ut+div g(u) = 0, u(0, ·) = u0 and of the evolutionary integral equation (k * (u-u0))t+div g(u) = 0 are given in terms of k, g and u0. A corresponding result is obtained for more general evolution equations with an accretive non-linearity.",

author = "B. Cockburn and G. Gripenberg and Londen, \{S. O.\}",

note = "Funding Information: * Partially supported by NSF Grant DMS-94-07952. E-mail: cockburn -E-mail: Gustaf.Gripenberg helsinki.fi. E-mail: Stig-Olof.Londen hut.fi.",

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N2 - Estimates of the difference between the entropy solutions of the single conservation law ut+div g(u) = 0, u(0, ·) = u0 and of the evolutionary integral equation (k * (u-u0))t+div g(u) = 0 are given in terms of k, g and u0. A corresponding result is obtained for more general evolution equations with an accretive non-linearity.

AB - Estimates of the difference between the entropy solutions of the single conservation law ut+div g(u) = 0, u(0, ·) = u0 and of the evolutionary integral equation (k * (u-u0))t+div g(u) = 0 are given in terms of k, g and u0. A corresponding result is obtained for more general evolution equations with an accretive non-linearity.

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On convergence to entropy solutions of a single conservation law

Abstract

Bibliographical note

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