Selection, shape, and relaxation of fronts: a numerical study of the effects of inertia

We study the problem of front propagation in the presence of inertia. We extend the analytical approach for the overdamped problem to this case, and present numerical results to support our theoretical predictions. Specifically, we conclude that the velocity and shape selection problem can still be described in terms of the metastable, nonlinear, and linear overdamped regimes. We study the characteristic relaxation dynamics of these three regimes, and the existence of degenerate ("quenched") solutionsWork at Barcelona was supported by DGES (Spain) through Grant Nos. PB96-0241 and BFM2000-0624. Work at Leganés was supported by DGES (Spain) through Grant No. PB96-0119 and DGI ~Spain! through Grant No. BFM2000-0006.Publicad