5 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…
Best Approximations on Quasi-Cone Metric Spaces
Ahmad Hisbu Zakiyudin, Kistosil Fahim, Nur Millatul Af-Idah +4
This paper focuses on the best approximation in quasi-cone metric spaces, a combination of quasi-metrics and cone metrics, which generalizes the notion of distance by allowing it t…
Yamada-Watanabe uniqueness results for SPDEs driven by Wiener and pure jump processes
Kistosil Fahim, Erika Hausenblas, Kenneth H. Karlsen
The Yamada-Watanabe theory provides a robust framework for understanding stochastic equations driven by Wiener processes. Despite its comprehensive treatment in the literature, the…
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…
Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise
Erika Hausenblas, Mihály Kovács
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when consi…