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    On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

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    Type
    Article
    Authors
    Antonelli, Paolo
    Markowich, Peter A. cc
    Obermeyer, Ryan cc
    Sierra, Jesus
    SPARBER, CHRISTOF
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-10-02
    Online Publication Date
    2019-10-02
    Print Publication Date
    2019-11-01
    Permanent link to this record
    http://hdl.handle.net/10754/660402
    
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    Abstract
    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/ab2bc1
    Sponsors
    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 Publishing
    Journal
    Nonlinearity
    DOI
    10.1088/1361-6544/ab2bc1
    Additional Links
    https://iopscience.iop.org/article/10.1088/1361-6544/ab2bc1
    ae974a485f413a2113503eed53cd6c53
    10.1088/1361-6544/ab2bc1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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