Two scale hydrodynamic limit for a model of malignant tumor cells
Anna De Masi, Stephan Luckhaus, and Errico Presutti
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Submission date: 05. Jan. 2005
published in: Annales de l'Institut Henri Poincaré / B, 43 (2007) 3, p. 257-297
DOI number (of the published article): 10.1016/j.anihpb.2006.03.003
MSC-Numbers: 60K35, 35K57
Keywords and phrases: two scale hydodynamic limit limit, exclusion process
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We look at a lattice model introduced by Luckhaus and Triolo for competition beetween normal and malignant cells.Malignant cells are diffusing fast whereas normal cells move on a slower scale and obey an exclusion rule.The difference in time scales allows to derive a two scale hydrodynamic limit.A key ingredient of the proof is to reproduce the parabolic a priori estimates on the level of generators of the stochastic process.