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SUMMARY:Stable undular bores - Vera Mikyoung Hur (University of Illinois a
 t Urbana-Champaign)
DTSTART:20220905T093000Z
DTEND:20220905T103000Z
UID:TALK177806@talks.cam.ac.uk
DESCRIPTION:I will discuss the global nonlinear asymptotic stability of th
 e traveling front solutions to the Korteweg-de Vries--Burgers equation\, a
 nd for a general class of dispersive-dissipative perturbations of the Burg
 ers equation. Earlier works made strong use of the monotonicity of the fro
 nt\, for relatively weak dispersion effects. We instead exploit the modula
 tion of the translation parameter of the front solution\, establishing a n
 ew stability criterion that a certain Schrodinger operator in one dimensio
 n has exactly one negative eigenvalue\, so that a rank-one perturbation of
  the operator can be made positive definite. Counting the number of bound 
 states of the Schrodinger equation\, we find a sufficient condition in ter
 ms of a Bargman-type functional\, related to the area between the front an
 d the corresponding ideal shock. We analytically verify that our stability
  criterion is met for an open set including all monotone fronts. Our numer
 ical experiments\, revealing more stable fronts\, suggest a computer-assis
 ted proof. Joint with Blake Barker\, Jared Bronski\, and Zhao Yang.
LOCATION:Seminar Room 1\, Newton Institute
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