An explicit solution of Burgers equation with stationary point source

Jaywan Chung, Yong-Jung Kim, Marshall Slemrod
2014 Journal of Differential Equations  
The purpose of this article is to introduce a diffusion model for biological organisms that increase their motility if food or resource is not enough. It is shown in this paper that Fick's diffusion law does not give such a starvation (or need) driven diffusion correctly. The diffusion model for non-uniform Brownian motion or non-uniform random walk in [1,2] is employed and a Fokker-Planck type diffusion law is obtained as the result. Lotka-Volterra competition systems for two species are
more » ... , where one species follows the starvation driven diffusion and the other follows the linear diffusion. The starvation driven diffusion turns out to be a better survival strategy than the linear one in heterogeneous environments. Various issues such as the global asymptotic stability, convergence to an ideal free distribution, the extinction and coexistence are discussed.
doi:10.1016/j.jde.2014.05.046 fatcat:jb4ki3inp5e4hoqxjrmntsne3i