Journal of Evolution Equations

, Volume 18, Issue 4, pp 1713–1720 | Cite as

Global existence for reaction–diffusion systems with dissipation of mass and quadratic growth

  • Philippe SoupletEmail author


We consider the Neumann and Cauchy problems for positivity preserving reaction–diffusion systems of m equations enjoying the mass and entropy dissipation properties. We show global classical existence in any space dimension, under the assumption that the nonlinearities have at most quadratic growth. This extends previously known results which, in dimensions \(n\ge 3\), required mass conservation and were restricted to the Cauchy problem. Our proof is also simpler.


Reaction–diffusion systems Mass dissipation Entropy Global existence 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Paris 13, Sorbonne Paris Cité, CNRS UMR 7539, Laboratoire Analyse Géométrie et ApplicationsVilletaneuseFrance

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