4 papers
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…
A discrete data assimilation algorithm for the reconstruction of Gray--Scott dynamics
Tsiry Avisoa Randrianasolo
The Gray--Scott model governs the interaction of two chemical species via a system of reaction-diffusion equations. Despite its simple form, it produces extremely rich patterns suc…
Convergence and error analysis of a semi-implicit finite volume scheme for the Gray--Scott system
Tsiry Avisoa Randrianasolo
We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of…
Numerical approximation of Dynkin games with asymmetric information
ĽubomÃr BaÅas, Giorgio Ferrari, Tsiry Avisoa Randrianasolo
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum d…