BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Pattern selection in reaction-diffusion-ODE and mechanochemical sy
 stems [Oberseminar Analysis]
DTSTART:20261113T131500Z
DTEND:20261113T151500Z
DTSTAMP:20261111T130700Z
UID:indico-event-1777@math-events.uni-bonn.de
DESCRIPTION:Speakers: Finn Münnich (University Heidelberg)\n\n Spontaneo
 us pattern formation is classically explained by Turing's diffusion-driven
  instability (DDI)\, typically realised by a slowly diffusing activator an
 d a fast-diffusing inhibitor. In this talk\, I discuss two settings beyond
  this classical picture and ask\, in each\, which pattern is actually sele
 cted.First\, I consider reaction-diffusion systems in which some component
 s do not diffuse\, so-called reaction-diffusion-ODE systems. Their station
 ary solutions can be less regular than in classical reaction-diffusion sys
 tems\, exhibiting for example jump discontinuities\, and the linearised op
 erator has nontrivial essential spectrum. I derive sufficient conditions f
 or DDI in systems with three spatial scales (non-diffusing\, slow- and fas
 t-diffusing components)\, and show that the destabilisation mechanism infl
 uences the stability of the emerging patterns. I also construct patterns w
 ith jump discontinuities\, which exist largely independently of the diffus
 ion coefficients. Deciding between regular and jump-discontinuous patterns
  requires a nonlinear stability theory for bounded\, possibly discontinuou
 s\, steady states. I show that\, in the space of bounded functions\, a neg
 ative spectral bound of the linearisation implies nonlinear stability and 
 a positive one implies instability\, without requiring a spectral gap.Seco
 nd\, I present a mechanochemical model for head formation in the freshwate
 r polyp Hydra\, in which tissue mechanics takes the role of the fast-diffu
 sing inhibitor. A one-dimensional reduction leads to a nonlocal reaction-d
 iffusion equation\, for which only single-peak patterns can be stable\, co
 nsistent with the single body axis of Hydra. A bifurcation analysis reveal
 s subcritical branches and bistability between the constant state and nonc
 onstant stationary solutions\, so that in this regime patterns emerge only
  from sufficiently large perturbations of the homogeneous state.Based on j
 oint work with T. André\, S. Cygan\, C. Kowall\, A. Marciniak-Czochra and
  D. Oelz.\n\nhttps://math-events.uni-bonn.de/event/1777/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1777/
END:VEVENT
END:VCALENDAR