5 papers
Time-asymptotic self-similarity of the damped compressible Euler equations in parabolic scaling variables
Thomas Eiter, Stefanie Schindler
We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the d…
Convergence to self-similar profiles in reaction-diffusion systems
Alexander Mielke, Stefanie Schindler
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe differe…
Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States
Alexander Mielke, Stefanie Schindler
We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a fini…
Existence of similarity profiles for diffusion equations and systems
Alexander Mielke, Stefanie Schindler
We study the existence of similarity profiles for diffusion equations and reaction diffusion systems on the real line, where the different nontrivial limits are imposed for $ x \to…
Gradient flows for bounded linear evolution equations
D. R. Michiel Renger, Stefanie Schindler
We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient f…