Global-in-time behavior of weak solutions to reaction-diffusion systems with inhomogeneous Dirichlet boundary condition

Michel Pierre 1, 2, 3, * Takashi Suzuki 4 Haruki Umakoshi 4
* Auteur correspondant
1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ENS Rennes - École normale supérieure - Rennes
3 UBL - Université Bretagne Loire
4 Graduate School of Engineering, Osaka University
Abstract : We study reaction diffusion systems describing, in particular, the evolution of concentrations in general reversible chemical reactions. We concentrate on inhomogeneous Dirichlet boundary conditions. We first prove global existence of (very) weak solutions. Then, we prove that these-although rather weak-solutions converge exponentially in L 1 norm toward the homogeneous equilibrium. These results are proven by means of L 2-duality arguments and through estimates provided by the nonincreasing entropy.
Keywords : convergence to equilibrium entropy global existence Dirichlet conditions asymptotic behavior reaction diffusion systems
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Article dans une revue
Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2017, 159, pp.393-407. <10.1016/j.na.2017.01.013>
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Contributeur : Michel Pierre <>
Soumis le : mardi 25 octobre 2016 - 17:04:19
Dernière modification le : lundi 17 juillet 2017 - 13:50:10

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Michel Pierre, Takashi Suzuki, Haruki Umakoshi. Global-in-time behavior of weak solutions to reaction-diffusion systems with inhomogeneous Dirichlet boundary condition. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2017, 159, pp.393-407. <10.1016/j.na.2017.01.013>. <hal-01387543>

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