Some theory in many component reaction-diffusion systems including activator and inhibitor

Many component non-linear partial integro-differential equations, mainly of reaction diffusion type, are considered. Results are obtained, e. g., for linear stability analysis of stationary structures including steep parts, here called fronts. For linear stability analysis singualr and regular perturbation techniques are developed. Main results are eigenvalue equations for critical eigenvalues, i. e. for eigenvalues, the real parts of which are close to zero and cross zero when varying parameters. I. e., main topic is destabilization and/or stabilization of front structures.