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L 1-Framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations

Abstract:

We develop a general L 1-framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach. We apply our L 1-framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without imposition of bounded variation of the approximate solutions. Finally, as an example of a direct appl...

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Journal:
Transactions of the American Mathematical Society
Volume:
358
Issue:
3
Pages:
937-963
Publication date:
2006-03-01
DOI:
ISSN:
0002-9947
Source identifiers:
203272
Language:
English
Keywords:
Pubs id:
pubs:203272
UUID:
uuid:c6fdc125-0161-49a7-a6c2-86f41751f852
Local pid:
pubs:203272
Deposit date:
2012-12-19

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