@article{FeireislKlingenbergMarkfelder2020,
  author    = {Feireisl, Eduard and Klingenberg, Christian and Markfelder, Simon},
  title     = {On the density of "wild" initial data for the compressible Euler system},
  series = {Calculus of Variations and Partial Differential Equations},
  volume    = {59},
  journal   = {Calculus of Variations and Partial Differential Equations},
  issn      = {0944-2669},
  doi       = {10.1007/s00526-020-01806-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232607},
  year      = {2020},
  abstract  = {We consider a class of "wild" initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural L1-topology and show that its complement is rather large, specifically it is an open dense set.},
  language  = {en}
}
@article{LauerbachNeukammSchaeffneretal.2019,
  author    = {Lauerbach, Laura and Neukamm, Stefan and Sch{\"a}ffner, Mathias and Schl{\"o}merkemper, Anja},
  title     = {Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems - Fracture in Composite Materials},
  series = {Proceedings in Applied Mathematics \& Mechanics},
  volume    = {19},
  journal   = {Proceedings in Applied Mathematics \& Mechanics},
  number    = {1},
  doi       = {10.1002/pamm.201900070},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211835},
  pages     = {e201900070},
  year      = {2019},
  abstract  = {The limiting behaviour of a one-dimensional discrete system is studied by means of Γ-convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard-Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of the problem, which yields a limiting energy of Griffith's type consisting of a quadratic integral term and a jump contribution. The periodic case can be found in [8], the stochastic case in [6,7].},
  language  = {en}
}
@article{FallMinlendRatzkin2022,
  author    = {Fall, Mouhammed Moustapha and Minlend, Ignace Aristide and Ratzkin, Jesse},
  title     = {Foliation of an Asymptotically Flat End by Critical Capacitors},
  series = {The Journal of Geometric Analysis},
  volume    = {32},
  journal   = {The Journal of Geometric Analysis},
  number    = {2},
  issn      = {1559-002X},
  doi       = {10.1007/s12220-021-00746-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269997},
  year      = {2022},
  abstract  = {We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the nonlocal nature of our problem.},
  language  = {en}
}
@article{EastonvanDalenGoebetal.2022,
  author    = {Easton, Andrew and van Dalen, Okki and Goeb, Rainer and Di Bucchianico, Alessandro},
  title     = {Bivariate copula monitoring},
  series = {Quality and Reliability Engineering International},
  volume    = {38},
  journal   = {Quality and Reliability Engineering International},
  number    = {3},
  doi       = {10.1002/qre.3034},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-276501},
  pages     = {1272 -- 1288},
  year      = {2022},
  abstract  = {The assumption of multivariate normality underlying the Hotelling T\(^{2}\) chart is often violated for process data. The multivariate dependency structure can be separated from marginals with the help of copula theory, which permits to model association structures beyond the covariance matrix. Copula-based estimation and testing routines have reached maturity regarding a variety of practical applications. We have constructed a rich design matrix for the comparison of the Hotelling T\(^{2}\) chart with the copula test by Verdier and the copula test by Vuong, which allows for weighting the observations adaptively. Based on the design matrix, we have conducted a large and computationally intensive simulation study. The results show that the copula test by Verdier performs better than Hotelling T\(^{2}\) in a large variety of out-of-control cases, whereas the weighted Vuong scheme often fails to provide an improvement.},
  language  = {en}
}
@article{GathunguBorzi2017,
  author    = {Gathungu, Duncan Kioi and Borz{\`i}, Alfio},
  title     = {Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator},
  series = {Applied Mathematics},
  volume    = {8},
  journal   = {Applied Mathematics},
  number    = {7},
  doi       = {10.4236/am.2017.87076},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-158525},
  pages     = {967-986},
  year      = {2017},
  abstract  = {An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.},
  language  = {en}
}
@article{KienleGarridoBreitenbachChudejetal.2018,
  author    = {Kienle-Garrido, Melina-Lor{\´e}n and Breitenbach, Tim and Chudej, Kurt and Borz{\`i}, Alfio},
  title     = {Modeling and numerical solution of a cancer therapy optimal control problem},
  series = {Applied Mathematics},
  volume    = {9},
  journal   = {Applied Mathematics},
  number    = {8},
  doi       = {10.4236/am.2018.98067},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-177152},
  pages     = {985-1004},
  year      = {2018},
  abstract  = {A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an "interior point optimizer―a mathematical programming language" (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.},
  language  = {en}
}
@article{CampanaBorzi2022,
  author    = {Campana, Francesca Cal{\`a} and Borz{\`i}, Alfio},
  title     = {On the SQH Method for Solving Differential Nash Games},
  series = {Journal of Dynamical and Control Systems},
  volume    = {28},
  journal   = {Journal of Dynamical and Control Systems},
  issn      = {1573-8698},
  doi       = {10.1007/s10883-021-09546-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269111},
  pages     = {739-755},
  year      = {2022},
  abstract  = {A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method is formulated in the framework of the Pontryagin maximum principle and represents an efficient and robust extension of the successive approximations strategy for solving optimal control problems. Theoretical results are presented that prove the well-posedness of the proposed scheme, and results of numerical experiments are reported that successfully validate its computational performance.},
  language  = {en}
}
@article{KrausMouchaRoth2022,
  author    = {Kraus, Daniela and Moucha, Annika and Roth, Oliver},
  title     = {A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights},
  series = {Analysis and Mathematical Physics},
  volume    = {12},
  journal   = {Analysis and Mathematical Physics},
  number    = {1},
  issn      = {1664-235X},
  doi       = {10.1007/s13324-021-00639-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-270485},
  year      = {2022},
  abstract  = {We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301-3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weights. In the scalar case this new upper bound is optimal.},
  language  = {en}
}
@article{HomburgWeissAlwanetal.2021,
  author    = {Homburg, Annika and Weiß, Christian H. and Alwan, Layth C. and Frahm, Gabriel and G{\"o}b, Rainer},
  title     = {A performance analysis of prediction intervals for count time series},
  series = {Journal of Forecasting},
  volume    = {40},
  journal   = {Journal of Forecasting},
  number    = {4},
  doi       = {10.1002/for.2729},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-217906},
  pages     = {603 -- 609},
  year      = {2021},
  abstract  = {One of the major motivations for the analysis and modeling of time series data is the forecasting of future outcomes. The use of interval forecasts instead of point forecasts allows us to incorporate the apparent forecast uncertainty. When forecasting count time series, one also has to account for the discreteness of the range, which is done by using coherent prediction intervals (PIs) relying on a count model. We provide a comprehensive performance analysis of coherent PIs for diverse types of count processes. We also compare them to approximate PIs that are computed based on a Gaussian approximation. Our analyses rely on an extensive simulation study. It turns out that the Gaussian approximations do considerably worse than the coherent PIs. Furthermore, special characteristics such as overdispersion, zero inflation, or trend clearly affect the PIs' performance. We conclude by presenting two empirical applications of PIs for count time series: the demand for blood bags in a hospital and the number of company liquidations in Germany.},
  language  = {en}
}
@article{Mitra2020,
  author    = {Mitra, Sourav},
  title     = {Local Existence of Strong Solutions of a Fluid-Structure Interaction Model},
  series = {Journal of Mathematical Fluid Mechanics},
  volume    = {22},
  journal   = {Journal of Mathematical Fluid Mechanics},
  issn      = {1422-6928},
  doi       = {10.1007/s00021-020-00520-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-235097},
  year      = {2020},
  abstract  = {We are interested in studying a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler-Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.},
  language  = {en}
}