Renormalized Dissipative Solutions for Quasilinear Anisotropic Degenerate Parabolic Equations

Satoru Takagi

Title	Renormalized Dissipative Solutions for Quasilinear Anisotropic Degenerate Parabolic Equations
Publication Type	Journal Article
Year of Publication	2005
Authors	Takagi, S
Volume	9
Issue	4
Start Page	481
Pagination	24
Date Published	2005
ISSN	1083-2564
AMS	35K45, 35K65, 47H06
Abstract	We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a quasilinear anisotropic degenerate parabolic equation ${ u_t+div F(u) = div (A(u)∇u)+f }$ with locally Lipschitz-continuous flux ${ F }$ and ${ L^1 }$ data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. As applications, we apply our result to certain relaxation systems in general ${L^1 }$ -setting and construct a renormalized dissipative solution.
URL	http://www.acadsol.eu/en/articles/9/4/4.pdf
Refereed Designation	Refereed
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