A note on uniqueness of entropy solutions to degenerate parabolic equations in $\mathbb{R}^N$. - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

A note on uniqueness of entropy solutions to degenerate parabolic equations in $\mathbb{R}^N$.

Résumé

We study the Cauchy problem in $\mathbb{R}^N$ for the parabolic equation $u_t+\text{div} F(u)=\Delta \varphi(u)$, which can degenerate into a hyperbolic equation for some intervals of values of $u$. In the context of conservation laws (the case $\varphi\equiv 0$), it is known that an entropy solution can be non-unique when $F'$ has strong singularities. We show the uniqueness of an entropy solution to the general parabolic problem for all $L^\infty$ initial datum, under the isotropic condition on the flux $F$ known for conservation laws. The only assumption on the diffusion term is that $\varphi$ is a non-decreasing continuous function.
Fichier principal
Vignette du fichier
PreprintAndreianovMaliki-ConvDiff-RN.pdf (153.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00378475 , version 1 (24-04-2009)
hal-00378475 , version 2 (05-09-2009)

Identifiants

  • HAL Id : hal-00378475 , version 1

Citer

Boris Andreianov, Mohamed Maliki. A note on uniqueness of entropy solutions to degenerate parabolic equations in $\mathbb{R}^N$.. 2009. ⟨hal-00378475v1⟩
211 Consultations
407 Téléchargements

Partager

Gmail Facebook X LinkedIn More