On the stability of nonlinear reaction-diffusion processes

The stability of a nonlinear reaction-diffusion process and its convergence rate can be determined very simply, based on an extension of the recently developed tools of contraction theory. This paper extend our earlier results [9] to the case where the diffusion term is itself nonlinear and where a convection term is also introduced. The results have applications to observer design for distributed processes, enhancement of video signals, and approximation networks for estimation and control.