Stability of non-constant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations

Abstract. In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differen-tial equations, describing spatially-distributed growth of clonal populations of precancerous cells, whose proliferation is controled by growth factors diffusing in the extracellular medium and binding to the cell surface. We extend the results on the existence of nonhomogenous stationary solutions obtained in [9] to a general Hill-type production function and full parameter set. Using spec-tral analysis and perturbation theory we derive conditions for the linearized stability of such spatial patterns. 1