@article{2132, abstract = {We consider discrete porous medium equations of the form ∂tρt=Δϕ(ρt), where Δ is the generator of a reversible continuous time Markov chain on a finite set χ, and ϕ is an increasing function. We show that these equations arise as gradient flows of certain entropy functionals with respect to suitable non-local transportation metrics. This may be seen as a discrete analogue of the Wasserstein gradient flow structure for porous medium equations in ℝn discovered by Otto. We present a one-dimensional counterexample to geodesic convexity and discuss Gromov-Hausdorff convergence to the Wasserstein metric.}, author = {Erbar, Matthias and Jan Maas}, journal = {Discrete and Continuous Dynamical Systems- Series A}, number = {4}, pages = {1355 -- 1374}, publisher = {Southwest Missouri State University}, title = {{Gradient flow structures for discrete porous medium equations}}, doi = {10.3934/dcds.2014.34.1355 }, volume = {34}, year = {2014}, }