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

摘要

In this paper we study pattern formation arising in a system of a singlereaction-diffusion equation coupled with subsystem of ordinary differentialequations, describing spatially-distributed growth of clonal populations ofprecancerous cells, whose proliferation is controled by growth factorsdiffusing in the extracellular medium and binding to the cell surface. Weextend the results on the existence of nonhomogenous stationary solutionsobtained in the previous work of one of the authors to a general Hill-typeproduction function and full parameter set. Using spectral analysis andperturbation theory we derive conditions for the linearized stability of suchspatial patterns.