The Cauchy problem for a strongly degenerate quasilinear equation

Andreu, F., Caselles, Vicent, and Mazón, J. M.. "The Cauchy problem for a strongly degenerate quasilinear equation." Journal of the European Mathematical Society 007.3 (2005): 361-393. <http://eudml.org/doc/277572>.

@article{Andreu2005,
abstract = {We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation $u_t=\operatorname\{div\}\mathbf \{a\}(u,Du)$, where $\mathbf \{a\}(z,\xi )=\nabla _\xi f(z,\xi )$, and $f$ is a convex function of $\xi $ with linear growth as $\Vert \xi \Vert \rightarrow \infty $, 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.},
author = {Andreu, F., Caselles, Vicent, Mazón, J. M.},
journal = {Journal of the European Mathematical Society},
keywords = {entropy solution; quasilinear parabolic equation; relativistic heat equation; flux limited diffusion equation; radiation hydrodynamics; entropy solution; relativistic heat equation, flux limited diffusion equation, radiation hydrodynamics},
language = {eng},
number = {3},
pages = {361-393},
publisher = {European Mathematical Society Publishing House},
title = {The Cauchy problem for a strongly degenerate quasilinear equation},
url = {http://eudml.org/doc/277572},
volume = {007},
year = {2005},
}

TY - JOUR
AU - Andreu, F.
AU - Caselles, Vicent
AU - Mazón, J. M.
TI - The Cauchy problem for a strongly degenerate quasilinear equation
JO - Journal of the European Mathematical Society
PY - 2005
PB - European Mathematical Society Publishing House
VL - 007
IS - 3
SP - 361
EP - 393
AB - We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation $u_t=\operatorname{div}\mathbf {a}(u,Du)$, where $\mathbf {a}(z,\xi )=\nabla _\xi f(z,\xi )$, and $f$ is a convex function of $\xi $ with linear growth as $\Vert \xi \Vert \rightarrow \infty $, 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.
LA - eng
KW - entropy solution; quasilinear parabolic equation; relativistic heat equation; flux limited diffusion equation; radiation hydrodynamics; entropy solution; relativistic heat equation, flux limited diffusion equation, radiation hydrodynamics
UR - http://eudml.org/doc/277572
ER -