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New l(1)-gradient type estimates of solutions to one-dimensional quasilinear parabolic systems

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Díaz Díaz, Jesús Ildefonso and Antontsev, S.N. (2010) New l(1)-gradient type estimates of solutions to one-dimensional quasilinear parabolic systems. Communications in contemporary mathematics, 12 (1). pp. 85-106. ISSN 0219-1997

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Abstract

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L(1)-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton-Jacobi or conservation laws type.


Item Type:Article
Uncontrolled Keywords:laminar hot gas; renormalized solutions; elliptic-equations; colder atmosphere; discharge; existence; space; L(1)-gradient estimates; quasilinear parabolic systems; first order hyperbolic systems
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Differential equations
ID Code:15050
Deposited On:27 Apr 2012 08:30
Last Modified:12 Dec 2018 15:07

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