On some delayed nonlinear parabolic equations modeling CO oxidation

Abstract

It is known that several features of many react ion-diffusion systems can be studied through an associated Complex Ginzburg-Landau Equation (CGLE). In particular, the study of the catalytic CO oxidation leads to the Krischer-Eiswirth-Ertl model, a nonlinear parabolic system, which can be controlled by a delayed feedback term. For the control of its uniform oscillations, we had already studied the corresponding delayed CGLE, developing first a pseudolinearization principle, of a very broad applicability, which led us to a range of parameters for the stability of those oscillations. In this work we first present some simulations which confirm the mentioned range of parameters, and gives other ranges for different behavior. Out of the setting of the CGLE, the dynamics is richer, so we present another method for the study of the existence, (monotonicity methods) and stability (with the pseudolinearization principle), directly for the mentioned parabolic system.