Fischer Group

Theory of Partial Differential Equations, Applied and Numerical Analysis

Diverse phenomena such as the motion of fluids or elastic objects, the evolution of interfaces, or the physics of quantum-mechanical particles are described accurately by partial differential equations. The Fischer group works on the mathematical analysis of partial differential equations that arise in the sciences, connecting also to areas like numerical analysis or probability.

Partial differential equations are a fundamental tool for the description of many phenomena in the sciences, ranging from the physics of continua like fluids or elastic solids over quantum mechanics to population biology. Julian Fischer and his group work on the mathematical aspects of partial differential equations. One of the group’s main themes is the mathematical justification of model simplifications: For example, an elastic material with a highly heterogeneous small-scale structure may in many cases be approximated as a homogeneous material. Likewise, a fluid with low compressibility may in many cases be approximated as ideally incompressible. To justify such approximations, the group derives rigorous estimates for the approximation error. The techniques they employ connect the analysis of PDEs with adjacent mathematical areas like numerical analysis and probability.


On this site:


Team


Current Projects

Effective behavior of random materials | Evolution of interfaces in fluid mechanics and solids | Structure of fluctuations in stochastic homogenization | Entropy-dissipative PDEs


Publications

Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. IST Austria. View

Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09). View

Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. 284(5), 253–283. View

Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. View

Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674. View

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Career

since 2017 Assistant Professor, IST Austria
2014 – 2016 Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2013 – 2014 Postdoc, University of Zurich, Switzerland
2013 PhD, University of Erlangen-Nürnberg, Germany


Selected Distinctions

2020 ERC Starting Grant
2020 ÖMG-Förderungspreis, Early-/Mid-Career-Award of the Austrian Mathematical Society
2015 Dr. Körper Prize, PhD Award of the GAMM


Additional Information

Open Julian Fischer’s website
Go to Mathematics at IST Austria website



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