L2L2-energy stability via new dependent variables for circumventing strongly nonlinear reaction terms

The paper concerns a pair of reaction-diffusion system of P.D.Es. which have strongly nonlinear reaction terms (in the dependent variables) and which do not involve cross-diffusion terms, under Robin boundary conditions. The introduction of new dependent variables (suitable linear combinations of the original ones) which effectively induce cross-diffusion terms allows one to: (i) characterize the high nonlinearities with hidden dissipation; (ii) determine a procedure for bypassing these nonlinearities in the L2L2-energy stability analysis; (iii) obtain Liapunov functionals guaranteeing the same conditions of linear stability. As an application, the L2L2-energy stability analysis of the Brusselator system is performed.