Title: Non Pattern Formation in Chemorepulsion
Abstract: In contrast to diffusion (random diffusion without orientation), chemotaxis is the biased movement of cells/particles toward the region that contains higher concentration of beneficial or lower concentration of unfavorable chemicals. The former often refers to the attractive chemotaxis and latter to the repulsive chemotaxis. Chemotaxis has been advocated as a leading mechanism to account for the morphogenesis and self-organization of a variety of biological coherent structures such as aggregates, fruiting bodies, clusters, spirals, spots, rings, labyrinthine patterns and stripes, which have been observed in experiments. In this talk, I will present some recent development on the rigorous analysis of a partial differential equation model arising from repulsive chemotaxis which is a system of conservation laws consisting of nonlinear and coupled parabolic and hyperbolic type PDEs. In particular, global wellposedness, large-time asymptotic behavior of classical solutions to such model are obtained which indicate that chemorepulsion problem of this type exhibits strong tendency against pattern formation. The results are consistent with general results for classical repulsive chemotaxis models.