Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10427116 | Nonlinear Analysis: Theory, Methods & Applications | 2005 | 33 Pages |
Abstract
We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u-diva(u,Du)=v, where 0⩽vâL1(RN)â©Lâ(RN), a(z,ξ)=âξf(z,ξ), and f is a convex function of ξ with linear growth as â¥Î¾â¥ââ, satisfying other additional assumptions. In particular, this class of equations includes the elliptic problems associated to a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics, respectively. In a second part of this work, using Crandall-Liggett's iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the corresponding parabolic Cauchy problem.
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Authors
F. Andreu, V. Caselles, J.M. Mazón,