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Solutions for a nonlocal conservation law with fading memory

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 ∞ while the initial data is only in L∞. Moreover, if the memory kernel depends on a relaxation parameter ε > 0 and tends to a delta measure weakly as measures when ε → 0+, then the global entropy sol...

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Journal:
Proceedings of the American Mathematical Society
Volume:
135
Issue:
12
Pages:
3905-3915
Publication date:
2007-12-05
DOI:
ISSN:
0002-9939
URN:
uuid:a2d161d6-889f-474d-b2de-847c3af4c6ab
Source identifiers:
203562
Local pid:
pubs:203562

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