Franz Achleitner

research interests

applications: fluid dynamics (water waves), anomalous diffusion, structural dynamics
evolution equations: (viscous) hyperbolic conservation laws, reaction-diffusion equations, kinetic equations
concepts: asymptotic behavior of solutions: (meta)stability, decay rates
methods: dynamical system theory, entropy/entropy-dissipation, energy estimates

publications

11. F. Achleitner: Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem, submitted.
10. C.M. Cuesta, F. Achleitner: Addendum to "Travelling waves for a non-local Korteweg-de Vries-Burgers equation" [J. Differential Equations 257 (2014), no. 3, 720--758], J. Differential Equations 262 (2017), 1155-1160.
9. F. Achleitner, A. Arnold, E. Carlen: On linear hypocoercive BGK models, book chapter in "From Particle Systems to Partial Differential Equations III", Volume 162 of the series Springer Proceedings in Mathematics & Statistics, Springer 2016.
8. F. Achleitner, A. Arnold, D. Stürzer: Large-time behavior in non-symmetric Fokker-Planck equations, Rivista di Matematica della Universit`a di Parma 6, No. 1 (2015), 1-68.
7. F. Achleitner, C. Kuehn: Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations, in Communications in Applied and Industrial Mathematics 6, No. 2 (2015).
6. F. Achleitner, C. Kuehn: Traveling waves for a bistable equation with nonlocal diffusion, Advances in Differential Equations 20, No. 9-10 (2015), 887-936.
5. F. Achleitner, C. Kuehn: On bounded positive stationary solutions for a nonlocal Fisher-KPP equation, Nonlinear Analysis 112 (2015), 15-29.
4. F. Achleitner, C.M. Cuesta, S. Hittmeir: Travelling waves for a non-local Korteweg-de Vries-Burgers equation, J. Differential Equations 257, No. 3 (2014), 720-758.
3. F. Achleitner, S. Hittmeir, C. Schmeiser: On nonlinear conservation laws regularized by a Riesz-Feller operator, in Proceedings of the conference on Hyperbolic Problems HYP2012 in Padova 2012, F. Ancona, A. Bressan, P. Marcati, A. Marson (eds.), AIMS 2014.
2. F. Achleitner, P. Szmolyan: Saddle-node bifurcation of viscous profiles, Physica D. Nonlinear Phenomena 241, No. 20 (2012), 1703-1717.
1. F. Achleitner, S. Hittmeir, C. Schmeiser: On nonlinear conservation laws with a nonlocal diffusion term, J. Differential Equations 250, No. 4 (2011), 2177-2196.

theses

a. F. Achleitner: "Bifurcation and stability of viscous shock waves in viscous conservation laws", doctoral thesis, Vienna University of Technology 2009.
b. F. Achleitner: "Spectral stability of small amplitude shock profiles of the Jin-Xin model", master thesis, Vienna University of Technology 2004.

honors

2015 Best Paper Award, Faculty of Mathematics & Geoinformation, Vienna University of Technology
2011 Best Paper Award, Faculty of Mathematics & Geoinformation, Vienna University of Technology

services

12/2012 Reporter of the MFO Workshop Classical and Quantum Mechanical Models of Many-Particle Systems, MFO Oberwolfach, Germany.

collaborators

Anton Arnold
Eric Carlen
Carlota M. Cuesta
Laurent Desvillettes
Sabine Hittmeir
Ansgar Jüngel
Christian Kühn
József Lörinczi
Christian Schmeiser
Dominik Stürzer
Peter Szmolyan
Yoshihiro Ueda
Adrian Viorel
Bruno Volzone
Masakazu Yamamoto