Communications in Mathematical Sciences

Volume 17 (2019)

Number 2

Improved duality estimates: time discrete case and applications to a class of cross-diffusion systems

Pages: 339 – 351



Thomas Lepoutre (Institut Camille Jordan, Université Claude Bernard Lyon, Villeurbanne, France)


We adapt the improved duality estimates for bounded coefficients derived by Canizo et al. to the framework of cross diffusion. Since the estimates can not be directly applied we need to derive a time discrete version of their results and apply it to an implicit semi-discretization in time of the cross diffusion systems. This leads to new global existence results for cross diffusion systems with bounded cross diffusion pressures and potentially superquadratic reaction.


cross diffusion, duality estimates, Rothe method

2010 Mathematics Subject Classification


Received 29 August 2018

Received revised 28 November 2018

Accepted 28 November 2018

Published 8 July 2019