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SUMMARY:A result of existence and uniqueness for the Allen-Cahn equation w
 ith singular potentials and dynamic boundary conditions - Luca Calatroni\,
  (Cambridge Centre for Analysis)
DTSTART:20121114T160000Z
DTEND:20121114T170000Z
UID:TALK40604@talks.cam.ac.uk
CONTACT:Kevin Crooks
DESCRIPTION:In this talk we will present well-posedness results for the so
 lution to an initial and boundary-value problem for an Allen-Cahn type equ
 ation describing the phenomenon of phase transition for a material contain
 ed in a bounded and regular domain. The nonlinearity appearing in the equa
 tion is frequently assumed to be a double-well potential. In the talk we w
 ill generalize such nonlinearity considering a possibly non-smooth potenti
 al with domain different from the whole real line. Such potentials are typ
 ically called _singular_ potentials. Even though the Allen-Cahn equation i
 s frequently coupled with homogeneous Neumann boundary conditions (which a
 re meant to represent the orthogonality of the interface to the boundary a
 nd the absence of mass flux)\, physicists have recently introduced the so-
 called _dynamic_ boundary conditions which take into account the kinetics 
 of the process on the boundary as well. In this talk we will consider simi
 lar boundary conditions where another singular potential appears. Both the
  uniqueness and the continuous dependence on data results hold in a quite 
 general setting\, whereas for the proof of the existence we need to enforc
 e our assumptions\, introducing a compatibility condition between the two 
 singular potentials. We prove the existence result by regularizing the non
 linearities using Yosida approximations and exploiting some _a priori_ est
 imates that allow us to pass to the limit thanks to compactness and monoto
 nicity results.\n\nThis is a joint work with Prof. Pierluigi Colli\, Unive
 rsity of Pavia.
LOCATION:MR14\, Centre for Mathematical Sciences
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