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X-WR-CALNAME:CMM
X-WR-CALDESC:Centro de Modelamiento Matemático
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DTSTART:20260902T112258
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UID:MEC-12b7417590649f75a8760636f6e42857@cmm.uchile.cl
DTSTART;TZID=America/Santiago:20260901T140000
DTEND;TZID=America/Santiago:20260901T180000
DTSTAMP:20260831T103805Z
CREATED:20260831
LAST-MODIFIED:20260831
PRIORITY:5
SEQUENCE:1
TRANSP:OPAQUE
SUMMARY:SIPo “Homogenization of wentzell boundary condition in heat equation with markovian switching”
DESCRIPTION:Abstract: \nConsider the heat equation on a closed domain with C 2 boundary, subject to a random Wentzell boundary condition modeling stickiness and elastic killing, with coefficients undergoing Markovian switching. We derive the quenched and annealed evolution equations of these systems, inboth forward and backward directions. We show that as the switching rate tends to infinity, thesystem converges in the quenched L1 -sense to a heat equation with deterministic Wentzell condition,whose parameters are determined by the stationary law of the driving continuous-time Markov chain.\nWe further quantify the quenched uniform-in-time L1-error between the fast-switching process andits homogenized limit, establishing a rigorous error bound. In particular, for the time-dilatation t/ε,this error is o(ε−1/6 ), while the error between their time marginals is o(ε−1/2 ), as ε → 0. Finally, we apply our results to a model of neuronal receptor dynamics, where strong and weak ligand bindingcorrespond to distinct boundary regimes governing neurotransmitter clearance.\nSpeaker: Alexis Anagnostakis (CMM, U. de Chile)\n \n
URL:https://www.cmm.uchile.cl/events/sipo-homogenization-of-wentzell-boundary-condition-in-heat-equation-with-markovian-switching/
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CATEGORIES:Seminarios
LOCATION:Sala John Von Neumann, 7th floor, Beauchef 851
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