Global martingale solutions for a stochastic population cross-diffusion system
arXiv:1806.01124 · doi:10.1016/j.spa.2018.11.001
Abstract
The existence of global nonnegative martingale solutions to a stochastic cross-diffusion system for an arbitrary but finite number of interacting population species is shown. The random influence of the environment is modeled by a multiplicative noise term. The diffusion matrix is generally neither symmetric nor positive definite, but it possesses a quadratic entropy structure. This structure allows us to work in a Hilbert space framework and to apply a stochastic Galerkin method. The existence proof is based on energy-type estimates, the tightness criterion of Brzeźniak and co-workers, and Jakubowski's generalization of the Skorokhod theorem. The nonnegativity is proved by an extension of Stampacchia's truncation method due to Chekroun, Park, and Temam.
References in corpus (5)
- Global L_2-solutions of stochastic Navier-Stokes equations
- Local and global well-posedness of SPDE with generalized coercivity conditions
- Degenerate parabolic stochastic partial differential equations: Quasilinear case
- Global existence analysis of cross-diffusion population systems for multiple species
- Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation