RENORMALIZATION-GROUP THEORY AND VARIATIONAL CALCULATIONS FOR PROPAGATING FRONTS

We study the propagation of uniformly translating fronts into a linear ly unstable state, both analytically and numerically. We introduce a p erturbative renormalization group approach to compute the change in th e propagation speed when the fronts are perturbed by structural modifi cation of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely t he (numerical) experimentally observable propagation speed. For conven ience and completeness, the structural stability argument is also brie fly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the a ssumption of physical renormalizability. We also implement a variation al principle, due to Hadeler and Rothe [J. Math. Biol. 2, 251 (1975)], which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transitio n from ''linear marginal stability'' to ''nonlinear marginal stability '' as parameters in the governing equation are varied.