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X-WR-CALNAME:Claremont Center for the Mathematical Sciences
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X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences
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TZOFFSETFROM:-0800
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DTSTART:20180311T100000
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DTSTART;TZID=America/Los_Angeles:20180927T131500
DTEND;TZID=America/Los_Angeles:20180927T141500
DTSTAMP:20201128T085953
CREATED:20180925T052200Z
LAST-MODIFIED:20180926T052538Z
UID:619-1538054100-1538057700@colleges.claremont.edu
SUMMARY:Reaction-Diffusion Equations under Perturbations of the Domain (Professor Jose Arrieta\, Universidad Complutense de Madrid\, Spain)
DESCRIPTION:We analyze the behavior of the asymptotic dynamics of dissipative reaction-diffusion equations with Neumann boundary conditions when the domain where the equation is posed undergoes certain perturbation. We will focus on the behavior of the stationary solutions\, their local unstable manifolds and the attractors. \nWe will consider “regular” perturbations of the domain\, that is\, perturbations for which the spectra of the Laplace operator behaves continuously. In this case\, it turns out that if all the equilibria of the unperturbed system are nondegenerate (hyperbolic)\, then both the equilibria and their local unstable manifolds behave continuously under the perturbation. Exploiting the gradient properties of the flow we will show that the “attractors” also behave continuously. \nWe may also consider some “non-regular” perturbations of the domain. In this situation\, the problem needs to be studied and the technique adapted for each particular case. An interesting example of non regular perturbations is the “dumbbell domain” which consists in two domains joined by a very thin channel which degenerates to a line segment. We will describe the results obtained for this perturbation. \n
URL:https://colleges.claremont.edu/ccms/event/reaction-diffusion-equations-under-perturbations-of-the-domain/
LOCATION:Shanahan 3465\, Harvey Mudd College\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Special Event
ORGANIZER;CN="Alfonso%20Castro":MAILTO:castro@g.hmc.edu
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