7 papers
Sphere Constraints and Harmonic Map Flow: Controllability and Reachability by Low-Mode Forcing
Debopriya Mukherjee, Kistosil Fahim, Erika Hausenblas
We study the controllability and reachability of sphere-constrained evolution equations under degenerate (low-mode) forcing, with the harmonic map heat flow as the principal applic…
A stochastic Schauder-Tychonoff type theorem and its applications
Erika Hausenblas, Ankit Kumar, Jonas M. Tölle
One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stocha…
A Schauder-Tychonoff fixed-point approach for nonlinear Lévy driven reaction-diffusion systems
Erika Hausenblas, Michael A. Högele, Fahim Kistosil
We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion…
Reduced dynamics for models of pattern formation
Erika Hausenblas, Tsiry Avisoa Randrianasolo
The goal of this work is to analyze the long-term behavior of reaction-diffusion systems arising in two-species chemical models and to identify finite sets of modes that determine…
Weak solutions for coupled reaction-diffusion systems with pattern formation by a stochastic fixed point theorem
Erika Hausenblas, Michael A. Högele, Tesfalem A. Tegegn
Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. Thes…
Time discretization of a semi-discrete scheme for 3D Chemotaxis-Navier-Stokes system driven by transport noise
Erika Hausenblas, Boris Jidjou Moghomye, Paul Andre Razafimandimby
This work is devoted to the convergence of a time-discrete numerical scheme of a semi-discretization model arising from biology, consisting of a chemotaxis equation coupled with a…