Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository

Florian Caro; Bilal Saad; Mazen Saad

doi:10.3934/dcdss.2014.7.191

Article Contents

2014, Volume 7, Issue 2: 191-205. Doi: 10.3934/dcdss.2014.7.191

This issue Previous Article Preface: Workshop in fluid mechanics and population dynamics Next Article From particles scale to anomalous or classical convection-diffusion models with path integrals

Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository

1.
CEA Saclay, DEN/DANS/DM2S/SFME/LSET5, 91191 Gif Sur Yvette
2.
King Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences & Engineering, 23955-6900, Thuwal
3.
Ecole Centrale de Nantes, Département d' Informatique et Mathématiques, Laboratoire de Mathématiques Jean Leray (UMR 6629 CNRS), 1, rue de la Noé, BP 92101

Received: March 31, 2013

Revised: June 30, 2013

Published: March 2014

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Abstract

Our goal is the mathematical analysis of a two phase (liquid and gas) two components (water and hydrogen) system modeling the hydrogen displacement in a storage site for radioactive waste. We suppose that the water is only in the liquid phase and is incompressible. The hydrogen in the gas phase is supposed compressible and could be dissolved into the water with the Henry law. The flow is described by the conservation of the mass of each components. The model is treated without simplified assumptions on the gas density. This model is degenerated due to vanishing terms. We establish an existence result for the nonlinear degenerate parabolic system based on new energy estimate on pressures.

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Mathematics Subject Classification: 35K65, 35K55, 76S05.

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