# The Cauchy problem for a strongly degenerate quasilinear equation

F. Andreu; Vicent Caselles; J. M. Mazón

Journal of the European Mathematical Society (2005)

- Volume: 007, Issue: 3, page 361-393
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topAndreu, 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 -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.