Geodesic
The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
Journal of the European Mathematical Society, Tome 7 (2005) no. 3, pp. 361-393.

Voir la notice de l'article provenant de la source EMS Press

We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation ut​=diva(u,Du), where 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 includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.
DOI : 10.4171/jems/32
Classification : 35-XX, 00-XX
Keywords: entropy solution, quasilinear parabolic equation, relativistic heat equation, flux limited diffusion equation, radiation hydrodynamics 
@article{JEMS_2005_7_3_a3,
     author = {Fuensanta Andreu and Vicent Caselles and Jos\'e M. Maz\'on},
     title = {The {Cauchy} {Problem} for a {Strongly} {Degenerate} {Quasilinear} {Equation}},
     journal = {Journal of the European Mathematical Society},
     pages = {361--393},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2005},
     doi = {10.4171/jems/32},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/32/}
}
TY  - JOUR
AU  - Fuensanta Andreu
AU  - Vicent Caselles
AU  - José M. Mazón
TI  - The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
JO  - Journal of the European Mathematical Society
PY  - 2005
SP  - 361
EP  - 393
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/32/
DO  - 10.4171/jems/32
ID  - JEMS_2005_7_3_a3
ER  - 
%0 Journal Article
%A Fuensanta Andreu
%A Vicent Caselles
%A José M. Mazón
%T The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
%J Journal of the European Mathematical Society
%D 2005
%P 361-393
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/32/
%R 10.4171/jems/32
%F JEMS_2005_7_3_a3
Fuensanta Andreu; Vicent Caselles; José M. Mazón. The Cauchy Problem for a Strongly Degenerate Quasilinear Equation. Journal of the European Mathematical Society, Tome 7 (2005) no. 3, pp. 361-393. doi : 10.4171/jems/32. http://geodesic.mathdoc.fr/articles/10.4171/jems/32/

Cité par Sources :