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UID:2023092107055320230925T16000020230925T165000650c9411af6bc@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20230921T013820
DTSTART:20230925T160000
DTEND:20230925T165000
SUMMARY:Analysis and Applied Mathematics Seminar: Unconditional Stability of KdV-Burgers Fronts, by Jared Bronski
DESCRIPTION:Jared Bronski (University of Illinois Urbana-Champaign): Unconditional Stability of KdV-Burgers Fronts \[ u_t + u u_x = \eta u_{xxx} + u_{xx} \qquad \lim_{x \rightarrow \mp \infty }u = \pm 1 \] Originally proposed by Whitham as a model for the propagation of tidal bores. It was shown by Bona and Schonbek that front type traveling wave solutions exist for all $\eta$, unique modulo translation, and are monotone for $|\eta|\leq \frac14$, and by Pego that such solutions are stable to small perturbations for the monotone case. We present a new stability criteria that does not require a smallness assumption on the difference between the initial data and the traveling wave, and which can be shown to hold in an open set of $\eta$ values that includes the monotone case. This condition involves the number of bound states of a certain Schr\”dinger operator constructed from the front solution. We will also discuss some rigorous numerical calculations that give intervals in $\eta$ where this spectral condition is guaranteed to hold. Joint work with Blake Barker, Vera Hur and Zhao Yang. Please click here to make changes to, or delete, this seminar announcement. | Event post: https://mscs.uic.edu/events?page_id=5148172
LOCATION:636 SEO Chicago IL
CLASS:PRIVATE
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