{"author":[{"full_name":"Erbar, Matthias","first_name":"Matthias","last_name":"Erbar"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","full_name":"Jan Maas","orcid":"0000-0002-0845-1338"}],"date_published":"2014-04-01T00:00:00Z","publication_status":"published","status":"public","extern":1,"abstract":[{"lang":"eng","text":"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."}],"date_created":"2018-12-11T11:55:54Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1212.1129"}],"page":"1355 - 1374","doi":"10.3934/dcds.2014.34.1355  ","year":"2014","day":"01","month":"04","issue":"4","publication":"Discrete and Continuous Dynamical Systems- Series A","volume":34,"intvolume":"        34","publisher":"Southwest Missouri State University","quality_controlled":0,"oa":1,"_id":"2132","citation":{"mla":"Erbar, Matthias, and Jan Maas. “Gradient Flow Structures for Discrete Porous Medium Equations.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 34, no. 4, Southwest Missouri State University, 2014, pp. 1355–74, doi:<a href=\"https://doi.org/10.3934/dcds.2014.34.1355  \">10.3934/dcds.2014.34.1355  </a>.","short":"M. Erbar, J. Maas, Discrete and Continuous Dynamical Systems- Series A 34 (2014) 1355–1374.","ama":"Erbar M, Maas J. Gradient flow structures for discrete porous medium equations. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2014;34(4):1355-1374. doi:<a href=\"https://doi.org/10.3934/dcds.2014.34.1355  \">10.3934/dcds.2014.34.1355  </a>","chicago":"Erbar, Matthias, and Jan Maas. “Gradient Flow Structures for Discrete Porous Medium Equations.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. Southwest Missouri State University, 2014. <a href=\"https://doi.org/10.3934/dcds.2014.34.1355  \">https://doi.org/10.3934/dcds.2014.34.1355  </a>.","ieee":"M. Erbar and J. Maas, “Gradient flow structures for discrete porous medium equations,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 34, no. 4. Southwest Missouri State University, pp. 1355–1374, 2014.","apa":"Erbar, M., &#38; Maas, J. (2014). Gradient flow structures for discrete porous medium equations. <i>Discrete and Continuous Dynamical Systems- Series A</i>. Southwest Missouri State University. <a href=\"https://doi.org/10.3934/dcds.2014.34.1355  \">https://doi.org/10.3934/dcds.2014.34.1355  </a>","ista":"Erbar M, Maas J. 2014. Gradient flow structures for discrete porous medium equations. Discrete and Continuous Dynamical Systems- Series A. 34(4), 1355–1374."},"date_updated":"2021-01-12T06:55:30Z","type":"journal_article","title":"Gradient flow structures for discrete porous medium equations","publist_id":"4903"}