Daniel Daners: Personal Front Page

General Information

I am an Associate Professor in the School of Mathematics and Statistics at The University of Sydney.

Contact Information

A/Prof Daniel Daners School of Mathematics and Statistics F07 The University of Sydney, NSW 2006 Australia   Office: Carslaw Building Room 715 Phone: +61 2 9351 2966 Fax: +61 2 9351 4534 Email: daniel.daners@sydney.edu.au

Research

I am a member of the Nonlinear Analysis Group. My interests are partial differential equations (particularly elliptic and parabolic boundary value problems), dynamical systems, analytic semigroup theory, operator theory.

You can look at my profiles on MathSciNet or view my profiles on Google Scholar or Zentralblatt Math.

Publication Highlights

Recent publications: (posted 16 April 2018):

• with J Glück, A criterion for the uniform eventual positivity of operator semigroups,
  Preprint arXiv:1801.05179, January 2018.
• with J López-Gómez, Global Dynamics of Generalized Logistic Equations,
  Advanced Nonlinear Studies 18 (2018), 217–236 (MR 3781305)
• with J Glück, Towards a perturbation theory for eventually positive semigroups,
  Preprint arXiv:1703.10108, March 2017, to appear in Journal of Operator Theory.
• with J Glück, The role of domination and smoothing conditions in the theory eventually positive semigroups,
  Preprint arXiv:1701.07309, January 2017, Bulletin of the Australian Mathematical Society 96 (2017), 286–298.
• with J Glück and JB Kennedy, Eventually and asymptotically positive semigroups on Banach lattices,
  Preprint arXiv:1511.05294, Journal of Differential Equations 261 (2016), 2607–2649.
• with Ch. Thornett, Periodic-parabolic eigenvalue problems with a large parameter and degeneration,
  Preprint, arXiv:1512.00485, Journal of Differential Equations 261 (2016), 273–295.

You can also look at my complete list of publications including preprints and links to the original articles if available.

Below some publication highlights.

• with P Koch Medina, Abstract evolution equations, periodic problems and applications, Longman Scientific & Technical, Harlow, Essex, 1992.
• Domain perturbation for linear and semi-linear boundary value problems, Handbook of Differential Equations: Stationary Partial Differential Equations, Vol 6, (2008), 1-81, Elsevier, 2008. ISBN-13: 978-0-444-53241-1.
• A Faber-Krahn inequality for Robin problems in any space dimension, Mathematische Annalen, 335 (2006), 767 - 785. (improvements with uniqueness and for p-Laplacian)
• Dirichlet problems on varying domains, J Diff Eq 188 (2003), 591-624. (related work)
• Heat kernel estimates for operators with boundary conditions, Math Nachr, 217(2000), 13-41.
• Robin boundary value problems on arbitrary domains, Trans AMS, 352 (2000), 4207-4236. (related work)
• with EN Dancer, Domain perturbation for elliptic equations subject to Robin boundary conditions, J Diff Eq 138 (1997), 86-132.
• Domain perturbation for linear and nonlinear parabolic equations, J Diff Eq 129 (1996), 358-402. (related work)

Professional Activities

• Organiser of 57th Annual Meeting of the Australian Mathematical Society at the University of Sydney
• Organiser of the Tohoku-Sydney Workshop on nonlinear PDE's for early career researchers on March 9, 2012 (joint with Tohoku Unversity)
• I help organise the AMSI-ANU Workshop on Spectral Theory (July 13-17, 2009)
• Organiser of special ession at the 7th Australia & New Zealand Mathematics Convention (with Yihong Du and Tom ter Elst)
• Organiser of special ession at the 50th Annual Meeting of the Australian Mathematical Society (with Xuan Duong and Xu-Jia Wang)
• Organiser of ICE-EM/AMSI Summer School 2007 (with Ruibin Zhang and Georg Gottwald)
• Organiser of conference Recent Advances in Nonlinear Partial Differential Equations at the University of New England from 16-21 July 2006 (with Yihong Du and Shusen Yan)

Courses Taught Recently

• MATH1921: Calculus of One variable (Advanced)
• MATH1901: Differential Integral Calculus (advanced)
• MATH1903: Integral Calculus and Modelling (advanced)
• MATH1906: Mathematics Special Studies Program
• MATH2961: Linear Algebra and Vector Calculus (Advanced)
• MATH2962: Real and Complex Analysis (Advanced)
• MATH3969: Measure Theory and Fourier Analysis (Advanced)

I am the coordinator for the first and second year Mathematics Special Studies Program (MATH1931/MATH1933 as well as MATH2916/MATH2917) and the Mathematics Talented Student Program.