Displaying similar documents to “Large time behaviour in convection-diffusion equations”

Exponential convergence to equilibrium Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Marzia Bisi, Laurent Desvillettes, Giampiero Spiga (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.


Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Marzia Bisi, Laurent Desvillettes, Giampiero Spiga (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.

Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations

José A. Carrillo, Lucas C. F. Ferreira (2006)

Banach Center Publications

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This work proves the convergence in L¹(ℝ²) towards an Oseen vortex-like solution to the dissipative quasi-geostrophic equations for several sets of initial data with suitable decay at infinity. The relative entropy method applies in a direct way for solving this question in the case of signed initial data and the difficulty lies in showing the existence of unique global solutions for the class of initial data for which all properties needed in the entropy approach are met. However, the...