% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@article{faucris.265989753,
abstract = {We derive an asymptotic expansion for the Weyl function of a one-dimensional Schrödinger operator which generalizes the classical formula by Atkinson. Moreover, we show that the asymptotic formula can also be interpreted in the sense of distributions.},
author = {Luger, Annemarie and Teschl, Gerald and Wöhrer, Tobias},
doi = {10.1007/s00605-015-0740-9},
faupublication = {no},
journal = {Monatshefte für Mathematik},
keywords = {Asymptotics; Distributional coefficients; Schrödinger operators; Weyl function},
note = {Created from Fastlane, Scopus look-up},
pages = {603-613},
peerreviewed = {Yes},
title = {{Asymptotics} of the {Weyl} function for {Schrödinger} operators with measure-valued potentials},
volume = {179},
year = {2016}
}
@article{faucris.265989500,
abstract = {The Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher’s equation. A detailed understanding of the large time behaviour of the solutions to these equations has been mostly achieved in the case where the relaxation function, measuring the intensity of the relaxation towards equally distributed velocity densities, is constant. The goal of the presented work is to provide a general method to tackle the question of convergence to equilibrium when the relaxation function is not constant, and to do so as quantitatively as possible. In contrast to the usual modal decomposition of the equations, which is natural when the relaxation function is constant, we define a new Lyapunov functional of pseudodifferential nature, one that is motivated by the modal analysis in the constant case, that is able to deal with full spatial dependency of the relaxation function. The approach we develop is robust enough that one can apply it to multi-velocity Goldstein-Taylor models, and achieve explicit rates of convergence. The convergence rate we find, however, is not optimal, as we show by comparing our result to those found in [8].},
author = {Arnold, Anton and Einav, Amit and Signorello, Beatrice and Wöhrer, Tobias},
doi = {10.1007/s10955-021-02702-8},
faupublication = {no},
journal = {Journal of Statistical Physics},
keywords = {BGK equation; Exponential decay; Hypocoercivity; Large time behaviour; Lyapunov functional},
note = {Created from Fastlane, Scopus look-up},
peerreviewed = {Yes},
title = {{Large} {Time} {Convergence} of the {Non}-homogeneous {Goldstein}-{Taylor} {Equation}},
volume = {182},
year = {2021}
}
@article{faucris.265988994,
abstract = {We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker–Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in time. The novelty of our study lies in the amalgamation of spectral theory and a quantitative non-symmetric hypercontractivity result, as opposed to the usual approach of the entropy method.},
author = {Arnold, Anton and Einav, Amit and Wöhrer, Tobias},
doi = {10.1016/j.jde.2018.01.052},
faupublication = {no},
journal = {Journal of Differential Equations},
keywords = {Fokker–Planck equations; Long time behaviour; Non-symmetric hypercontractivity; Spectral theory},
note = {Created from Fastlane, Scopus look-up},
pages = {6843-6872},
peerreviewed = {Yes},
title = {{On} the rates of decay to equilibrium in degenerate and defective {Fokker}–{Planck} equations},
volume = {264},
year = {2018}
}
@article{faucris.265989248,
abstract = {We review the Lyapunov functional method for linear ODEs and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defective ODE systems. As an application, we consider three evolution equations, namely the linear convection-diffusion equation, the two velocity BGK model and the Fokker–Planck equation. Adding an uncertainty parameter to the equations and analyzing its linear sensitivity leads to defective ODE systems. By applying the Lyapunov functional construction, we prove sharp long time behavior of order (1+t^{M})e^{−μt}, where M is the defect and μ is the spectral gap of the system. The appearance of the uncertainty parameter in the three applications makes it important to have decay estimates that are uniform in the non-defective limit.},
author = {Arnold, Anton and Jin, Shi and Wöhrer, Tobias},
doi = {10.1016/j.jde.2019.08.047},
faupublication = {no},
journal = {Journal of Differential Equations},
keywords = {Defective ODEs; Kinetic equations; Long time behavior; Lyapunov functionals; Sensitivity analysis; Uncertainty quantification},
month = {Jan},
note = {Created from Fastlane, Scopus look-up},
pages = {1156-1204},
peerreviewed = {Yes},
title = {{Sharp} decay estimates in local sensitivity analysis for evolution equations with uncertainties: {From} {ODEs} to linear kinetic equations},
volume = {268},
year = {2020}
}
@incollection{faucris.265887115,
author = {Wöhrer, Tobias and Dolbeault, Jean and Arnold, Anton and Schmeiser, Christian},
booktitle = {Recent Advances in Kinetic Equations and Applications},
doi = {10.1007/978-3-030-82946-9{\_}1},
faupublication = {yes},
peerreviewed = {unknown},
series = {Springer INdAM Series},
title = {{Sharpening} of decay rates in {Fourier} based hypocoercivity methods},
url = {https://link.springer.com/chapter/10.1007/978-3-030-82946-9{\_}1},
year = {2021}
}