Research

Research interests

My research is focused on Partial Differential Equations, Dynamical Systems and Applications in the Life Sciences (mainly in Biology, Physics and Physiology, e.g. in fluid dynamics and mathematical and computational cardiology and neuroscience, i.e. electrorheological fluids or early afterdepolarisations, respectively).

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Partial Differential Equations and Calculus of Variations:

• Parabolic equations and systems

• Obstacle problems

• Nonstandard growth problems

• Existence theory

• Regularity theory

  • Calderón-Zygmund theory

  • Higher integrability of solutions

  • Hölder regularity

• Stability theory

For a short introduction and a brief overview on in my research on PDEs, please see IV. Partial differential equations.

Dynamical Systems and Applied Mathematics in the Life Sciences:

• Dynamical systems

  • Bifurcation theory

  • Multiple Time Scale Dynamics (slow-fast system,...)

  • Geometric Singular Perturbation Theory (GSPT)

  • Numerical analysis and simulations using, e.g. MATLAB and MATCONT (bifurcation diagram, (critical) manifolds,...)

  • Ordinary differential Equations

• Applications in cardiology and neuroscience (on cellular level)

For a short introduction and a brief overview on in my research on dynamical systems and the investigation of cardiac arrhythmia, please see III. Dynamical Systems and Bifurcation Theory.

Interfaces of my two main research areas:

• Mathematical biology

• Mathematical modelling using partial and ordinary differential equations (e.g. heart or brain)

• Numerical analysis and simulations (on tissue level)

• Self-organising systems

• Wave pattern (travelling wave, spiral wave or wave breakup)