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SUMMARY:Tim Laux (University of Regensburg\, Germany)
DTSTART:20250227T150000Z
DTEND:20250227T160000Z
DTSTAMP:20260423T022055Z
UID:SIAM-PDE/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/51/
 ">The sharp-interface limit of the Allen-Cahn equation</a>\nby Tim Laux (U
 niversity of Regensburg\, Germany) as part of Seminar In the Analysis and 
 Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Allen-Cahn equation is one of
  the most basic reaction-diffusion equations\, modeling a large variety of
  phase transition problems. In a suitable scaling limit\, the transition b
 ecomes sharp and the system follows a geometric evolution equation - the m
 ean curvature flow. The structure of this "sharp-interface limit" has rece
 ived continuous attention from both the geometric and applied analysis com
 munities over the last decades. In this talk\, I will give an overview of 
 some of the breakthroughs in this field and highlight a recent short conve
 rgence analysis in a joint work with Julian Fischer and Theresa Simon. Our
  proof is based on a new relative entropy for diffuse interface problems t
 hat allows us to prove the optimal convergence rate toward mean curvature 
 flow.\n\nAtanas Stefanov\, University of Alabama\, Birminghan (stefanov@ua
 b.edu)\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/51/
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