Analysis and Applied Mathematics Seminar
Ryan Obermeyer
University of Illinois at Chicago
On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates
Abstract: We study a generalized dissipative Gross-Pitaevskii-type model
arising in the description of exciton-polariton condensates. We derive rigorous
existence and uniqueness results for this model posed on the one dimensional
torus and derive various a-priori bounds on its solution. Then, we analyze
in detail the long time behavior of spatially homogenous solutions and their
respective steady states. In addition, we will present numerical simulations in
the case of more general initial data. We also study the corresponding adiabatic
regime which results in a single damped-driven Gross-Pitaveskii equation and
compare its dynamics to the one of the full coupled system.
Joint work with C. Sparber, P. Antonelli, P. Markowich, and J. Sierra
Monday April 1, 2019 at 4:00 PM in 636 SEO