On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019-10-02Online Publication Date
2019-10-02Print Publication Date
2019-11-01Permanent link to this record
http://hdl.handle.net/10754/660402
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We 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.Citation
Antonelli, 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/ab2bc1Sponsors
The 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.Publisher
IOP PublishingJournal
NonlinearityAdditional Links
https://iopscience.iop.org/article/10.1088/1361-6544/ab2bc1ae974a485f413a2113503eed53cd6c53
10.1088/1361-6544/ab2bc1