Improved Duality Estimates and Applications to Reaction-Diffusion Equations

By José A. Cañizo, Laurent Desvillettes, Klemens Fellner. 2013

129 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/9b0a46921181fb49c7f5d2aa34fb5d9a643d75dc

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Citations in the corpus

The boundedness-by-entropy method for cross-diffusion systems (2015, background): “A global existence result for a system modeling the more general reaction A1+A2 ⇋ A3 + A4 was given in [11] in the two-dimensional case, the three-dimensional case being an open problem.”
Solutions of the 4-species quadratic reaction-diffusion system are bounded and C∞-smooth, in any space dimension (2017, background): “The result is extended for higher space dimensions in [7] which handles the quadratic case when the diffusion coefficients are close enough to the same constant (how small the distance between the dj ’s should be depends on the space dimension, in a explicit way), and in [8], which handles subquadra”
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems (2015, methodology): “[9] Laurent Desvillettes and Klemens Fellner.”
The boundedness-by-entropy principle for cross-diffusion systems (2014, background): “A global existence result for a system modeling the more general reaction A1 + A2 ⇋ A3 + A4 was given in [10] in the two-dimensional case, the three-dimensional case being an open”
Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations (2017, background): “Although the global existence of smooth solutions is conjectured for simple reaction-diffusion equations like (3) with a single reversible reaction with mass-action kinetics (2), there are no estimates available that would provide even just an L(1) bound for the reaction terms, even for smooth initi”