On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2019-10-02
Print Publication Date2019-11-01
Permanent link to this recordhttp://hdl.handle.net/10754/660402
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AbstractWe study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.
CitationAntonelli, P., Markowich, P., Obermeyer, R., Sierra, J., & Sparber, C. (2019). On a dissipative Gross–Pitaevskii-type model for exciton-polariton condensates. Nonlinearity, 32(11), 4317–4345. doi:10.1088/1361-6544/ab2bc1
SponsorsThe authors are grateful to the anonymous referee for helpful suggestions to improve upon an earlier version of this paper: in particular, we are grateful for pointing out the pointwise L∞-bound on n (see lemma 2.4) and for suggesting a Lyapunov-type functional similar to the one introduced in proposition 2.6.