2020/12/23 by Gaurav Dhariwal, Florian Huber, Dhariwal, Gaurav +3
Mathematics · Medicine · Social Sciences · #35Q92 #35R60 #60H15 #Analysis of PDEs (math.AP) #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2012.12765
openalex publication_date 2020/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The existence of global nonnegative martingale solutions to a cross-diffusion\nsystem of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven.\nThe model describes the segregation dynamics of populations with an arbitrary\nnumber of species. The diffusion matrix is generally neither symmetric nor\npositive semidefinite, which excludes standard methods. Instead, the existence\nproof is based on the entropy structure of the model, approximated by a\nWong-Zakai argument, and on suitable higher moment estimates and fractional\ntime regularity. In the case without self-diffusion, the lack of regularity is\novercome by carefully exploiting the entropy production terms.\n