Pattern propagation in nonlinear dissipative systems

We discuss the problem of pattern selection in situations where a stable, nonuniform state of a nonlinear dissipative system propagates into an initially unstable, homogeneous region. Our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known; and we point out that these known properties are consistent with a marginal-stability hypothesis that has been suggested in the theory of dendritic crystal growth. We then describe a more general interpretation of the marginal-stability hypothesis and, finally, present numerical evidence for its validity from three different pattern-forming models.