Improved duality estimates and applications to reaction-diffusion equations

Abstract

We present a refined duality estimate for parabolic equations. This estimate entails new results for systems of reaction-diffusion equations, including smoothness and exponential convergence towards equilibrium for equations with quadratic right-hand sides in two dimensions. For general systems in any space dimension, we obtain smooth solutions of reaction-diffusion systems coming out of reversible chemistry under an assumption that the diffusion coefficients are sufficiently close one to another.

References in corpus (1)

• Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

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• Close-to-equilibrium behaviour of quadratic reaction-diffusion systems with detailed balance
• Global existence analysis of energy-reaction-diffusion systems
• Quantitative dynamics of irreversible enzyme reaction-diffusion systems