I have seen the term spatial stability analysis in some papers. I know that stability is a property strongly linked with time. For instance, a solution $x^{*}$ is stable (in the sense of Lyapunov) if for any small perturbation the resulting perturbed trajectory $\tilde{x}$ remains sufficiently close to $x^{*}$ as time progress. Now, for spatio-temporal dynamics I have seen people talking about temporal stability analysis and spatial stability analysis. Does anyone know a source for the definition of the latter concept? does it exists a spatial Lyapunov theory-like for such analysis?
Many thanks in advance!