Entropy formulation of degenerate parabolic equation with zero-flux boundary condition - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

Entropy formulation of degenerate parabolic equation with zero-flux boundary condition

Résumé

We consider the general degenerate hyperbolic-parabolic equation: \begin{equation}\label{E}\tag{E} u_t+\div f(u)-\Delta\phi(u)=0 \mbox{ in } Q = (0,T)\times\Omega,\;\;\;\; T>0,\;\;\;\Omega\subset\mathbb R^N ; \end{equation} with initial condition and the zero flux boundary condition. Here $\phi$ is a continuous non decreasing function. Following [B\"{u}rger, Frid and Karlsen, J. Math. Anal. Appl, 2007], we assume that $f$ is compactly supported (this is the case in several applications) and we define an appropriate notion of entropy solution. Using vanishing viscosity approximation, we prove existence of entropy solution for any space dimension $N\geq 1$ under a partial genuine nonlinearity assumption on $f$. Uniqueness is shown for the case $N=1$, using the idea of [Andreianov and Bouhsiss, J. Evol. Equ., 2004], nonlinear semigroup theory and a specific regularity result for one dimension.
Fichier principal
Vignette du fichier
Article1.pdf (407.81 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00697593 , version 1 (15-05-2012)
hal-00697593 , version 2 (04-10-2012)

Identifiants

  • HAL Id : hal-00697593 , version 1

Citer

Boris Andreianov, Mohamed Karimou Gazibo. Entropy formulation of degenerate parabolic equation with zero-flux boundary condition. 2012. ⟨hal-00697593v1⟩
533 Consultations
258 Téléchargements

Partager

Gmail Facebook X LinkedIn More