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Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems

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Abstract

In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction–diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany

    J. Fischer

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Communicated by Alexander Mielke

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Fischer, J. Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems. Arch Rational Mech Anal 218, 553–587 (2015). https://doi.org/10.1007/s00205-015-0866-x

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