Prof. Dr. Heinrich Freistühler
Forschung
Heinrich Freistühlers Interessen betreffen die
Analysis und ihre Anwendungen, im einzelnen:
- Partielle Differentialgleichungen,
insbesondere hyperbolische Systeme von Erhaltungsleichungen
- singuläre Störungen und invariante Mannigfaltigkeiten
dynamischer Systeme,
-
Dynamik ein- oder mehrphasiger Kontinua,
- Stabilitätseigenschaften nichtlinearer Wellen,
insbesondere von Schockwellen und bewegten Phasengrenzen,
- hyperbolische Aspekte der relativistischen Fluiddynamik.
Aus diesen und verwandten Bereichen können auch Themen
für
Studienabschluss- oder Doktorarbeiten
vergeben werden.
Einige Publikationen:
H. F.:
Time-Asymptotic Stability for First-Order
Symmetric Hyperbolic Systems of Balance Laws
in Dissipative Compressible Fluid Dynamics.
To appear in Quart. Appl. Math.
H. F.: Relativistic barotropic fluids:
A Godunov-Boillat formulation for their
dynamics and a discussion of two special
classes. Arch. Ration. Mech. Anal., online first, 2018.
H. F. and Blake Temple:
Causal dissipation in the relativistic dynamics of barotropic
fluids. J. Math. Phys. 59 (2018), no. 6, 063101, 17 pp.
H. F.:
A relativistic version of the Euler-Korteweg equations. Methods Appl. Anal. 25
(2018), no. 1, 1-12.
H. F. and M. Kotschote:
Phase-field descriptions of
two-phase compressible fluid flow:
interstitial working and a reduction
to Korteweg theory. Q. Appl. Math., online first, 2018.
THIS IS A SUPPLEMENT TO ARMA 224 (2017), 1-20.
H. F. and Jan Fuhrmann: Nonlinear waves and polarization in
diffusive directed particle flow. SIAM J. Appl. Math. 78 (2018), 759-773.
H. F. and Blake Temple: Causal dissipation for the relativistic dynamics
of ideal gases. Proc. R. Soc. A 473 (2017), 20160729.
H.F., Felix Kleber, and Johannes Schropp: Emergence of
unstable modes for classical shock waves in isothermal ideal MHD.
Phys. D 358 (2017), 25-32
H.F. and Matthias Kotschote:
Phase-field and Korteweg-type models for the time-dependent flow of
compressible two-phase fluids. Arch. Ration. Mech. Anal. 224 (2017), 1-20.
Blake Barker, H.F., Kevin Zumbrun:
Convex entropy, Hopf bifurcation, and viscous and inviscid shock
stability. Arch. Ration. Mech. Anal. 217 (2015), no. 1, 309-372.
H.F. and Blake Temple:
Causal dissipation and shock profiles in the relativistic fluid dynamics of
pure radiation. Proc. R. Soc. Lond. Ser. A 470 (2014), 20140055.
H. F. and Yuri Trakhinin:
Symmetrizations of RMHD equations and stability of relativistic current-vortex sheets.
Classical and Quantum Gravity 30 (2013) 085012.
Martina Preusse, H.F., Frank Peeters: Seasonal variation of
solitary wave properties in Lake Constance. Journal of Geophysical Research: Oceans 117
(2012) C04026.
H.F. and Peter Szmolyan: Spectral stability of
small-amplitude viscous shock waves in several space dimensions.
Arch. Rational Mech. Anal. 195 (2010) 353-373.
H.F. and Yuri Trakhinin: On the viscous and inviscid
stability of magnetohydrodynamic shock waves. Physica D 237 (2008),
3030-3037.
H.F. and Mohammedreza Raoofi: Stability of
perfect-fluid
shock waves in special and general relativity. Classical and Quantum
Gravity
24 (2007), 4439-4455.
H.F. and Ramon G. Plaza:
Normal modes and nonlinear
stability behaviour of dynamic phase boundaries in elastic materials.
Arch. Rational Mech. Anal. 186 (2007), 1-24.
Sylvie Benzoni-Gavage and H.F.:
Effects of surface tension on the
stability of dynamical liquid-vapor interfaces.
Arch. Rational Mech. Anal.
174 (2004), 111-150.
H. F. and Christian Rohde: The bifurcation analysis of the MHD
Rankine-Hugoniot equations for a perfect gas. Physica D 185 (2003),
78-96.
H.F. and Denis Serre: L1 stability of shock waves in scalar
viscous conservation laws. Comm. Pure Appl. Math. 51 (1998), 291-301.
