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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2018

Cross-diffusion systems with non-zero flux and moving boundary conditions

Résumé

We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod-eling of a Physical Vapor Deposition process. Using the boundedness by entropy method introduced and developped in [5, 16], we prove the existence of a global weak solution to the obtained system. In addition, existence of a solution to an optimal control problem defined on the fluxes is established under the assumption that the solution to the considered cross-diffusion system is unique. Lastly, we prove that in the case when the imposed external fluxes are constant and positive and the entropy density is defined as a classical logarithmic entropy, the concentrations of the different species converge in the long-time limit to constant profiles at a rate inversely proportional to time. These theoretical results are illustrated by numerical tests.
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Dates et versions

hal-01397682 , version 1 (21-11-2016)
hal-01397682 , version 2 (08-09-2017)

Identifiants

  • HAL Id : hal-01397682 , version 2

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Athmane Bakhta, Virginie Ehrlacher. Cross-diffusion systems with non-zero flux and moving boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis, 2018. ⟨hal-01397682v2⟩
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