Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds

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Improved Duality Estimates and Applications to Reaction-Diffusion Equations (2013, methodology): “3) converge towards equilibrium exponentially fast (with explicitly computable constants) in any H norm (p ∈ ), thanks to interpolation arguments similar to those exposed in [10].”
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems (2015, unknown): “[8, 9, 10, 11, 29].”
Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations (2017, methodology): “The proof of the adjusted relative entropy inequality makes use of the following entropy dissipation estimate for renormalized solutions, which is also of independent interest as entropy dissipation inequalities may be used to analyze the long-time behavior of solutions (see [7, 8, 9, 10, 18, 30] an”