6533b83afe1ef96bd12a7817
RESEARCH PRODUCT
A strongly degenerate quasilinear elliptic equation
José M. MazónFuensanta AndreuVicent Casellessubject
Cauchy problemElliptic curveDiffusion equationElliptic partial differential equationApplied MathematicsMathematical analysisDegenerate energy levelsHeat equationUniquenessConvex functionAnalysisMathematicsMathematical physicsdescription
Abstract We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u - div a ( u , Du ) = v , where 0 ⩽ v ∈ L 1 ( R N ) ∩ L ∞ ( R N ) , a ( z , ξ ) = ∇ ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ∥ ξ ∥ → ∞ , 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-05-01 | Nonlinear Analysis: Theory, Methods & Applications |