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Elements of Calculus of Variations (Summer Semester 2023, Uni Ulm)

Partial Differential Equations (Summer Semester 2023, Uni Ulm)

Seminar with seminar paper on PDEs (Winter semester 2021, TU Vienna).

Transport Models for Semiconductors (2019, Charles University of Prague).

Lecture Notes

From the Boltzmann equation to hydrodynamic models (October 2017, Charles University of Prague).

Lecture Notes

Further references:

• M. Briant. On the Boltzmann equation, Quantitative studies and hydrodynamical limits. Doctoral dissertation, University of Cambridge, 2014.
• C. Cercignani, R. Illner and M. Pulvirenti. The mathematical theory of dilute gases. Vol. 106. Springer Science & Business Media, 2013.
• F. Golse. From kinetic to macroscopic models, 1998.

Entropy Methods for Diffusive PDEs (Summer semester 2017, TU Vienna).

Lecture Notes

Further references:

• A. Jüngel. Entropy Methods for Diffusive Partial Differential Equations. Springer, 2016.
• N. Zamponi, A. Jüngel. Global existence analysis for degenerate energy-transport models for semiconductors. Journal of Diff. Eq. 2015, vol. 258, 2339 - 2363.
• A. Jüngel, N. Zamponi. A cross-diffusion system derived from a Fokker-Planck equation with partial averaging. Z. Appl. Math. Phys. 68.1 (2017), 28.

Exercise classes for the course: Modelling with Partial Differential Equations (Winter semester 2016, TU Vienna).

Lecture notes: see link above.

Exercise sheets

Transport Models for Semiconductors (Summer semester 2015, TU Vienna).

Lecture Notes

Further references:

• A. Jüngel. Transport Equations for Semiconductors. Lecture Notes in Physics, Vol 773. Spinger, Berlin, 2009.
• N.W. Ashcroft, N. D. Mermin. Solid State Physics. Saunders College, Philadelfia, 1976.
• R. Shankar. Principles of Quantum Mechanics. Vol. 233, Plenum Press, New York, 1994.