| Abstract: |
| I will present recent conceptual results that establish that marginally stable fronts are selected in invasion problems, quite generally in parabolic systems. The result allows a conceptual approach to invasion problems, establishing existence of fronts, then marginal (spectral) stability, and concluding the selection of these fronts from localized initial conditions. The results do not rely on comparison principles in any form. We illustrate some first consequences by investigating transitions from pushed to pulled fronts, where marginal stability changes from point to essential spectrum, conceptually, numerically, and in a singularly perturbed example of logistic growth with negative taxis.
This is joint work with Montie Avery and Matt Holzer. |
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