Solutions for a nonlocal conservation law with fading memory
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- by Gui-Qiang Chen and Cleopatra Christoforou PDF
- Proc. Amer. Math. Soc. 135 (2007), 3905-3915 Request permission
Abstract:
Global entropy solutions in $BV$ for a scalar nonlocal conservation law with fading memory are constructed as the limits of vanishing viscosity approximate solutions. The uniqueness and stability of entropy solutions in $BV$ are established, which also yield the existence of entropy solutions in $L^\infty$ while the initial data is only in $L^\infty$. Moreover, if the memory kernel depends on a relaxation parameter $\varepsilon >0$ and tends to a delta measure weakly as measures when $\varepsilon \to 0+$, then the global entropy solution sequence in $BV$ converges to an admissible solution in $BV$ for the corresponding local conservation law.References
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Additional Information
- Gui-Qiang Chen
- Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
- MR Author ID: 249262
- ORCID: 0000-0001-5146-3839
- Email: gqchen@math.northwestern.edu
- Cleopatra Christoforou
- Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
- Address at time of publication: Department of Mathematics, University of Houston, Texas 77204-3008
- Email: cleo@math.northwestern.edu
- Received by editor(s): April 23, 2006
- Received by editor(s) in revised form: September 26, 2006
- Published electronically: September 7, 2007
- Communicated by: Walter Craig
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3905-3915
- MSC (2000): Primary 35L65, 35L60, 35K40
- DOI: https://doi.org/10.1090/S0002-9939-07-08942-3
- MathSciNet review: 2341940