Τhe resarch project iSTAMP is funded by the Hellenic Foundation for Research and Innovation (H.F.R.I) under the "First Call for H.F.R.I. Research Projects to support Faculty members and Researchers".

Stochastic partial differential equations (SPDEs) is an interdisciplinary area at the crossroads of stochastic processes and partial differential equations (PDEs). Generally speaking, any PDE is a SPDE if its coeffcients, forcing terms, initial and boundary conditions, or some of the above are random. The interaction between the theory of PDEs and probability is a very fruitful area for research in mathematics, both because of the intrinsic mathematical challenges presented, and because of the range of applications. The study of evolution equations with a stochastic forcing has seen major advances in the recent years. Applications include a variety of important nonlinear partial differential equations arising in mathematical physics, but the potential for development of this theory in other applications is enormous.

Mesoscopic models are either deterministic PDEs or SPDEs and typically they are viewed (although rarely rigorously derived) as large-scale limits of microscopic interacting particles systems. These models describe much larger space/time scales than the original microscopic model, and in the case where phase transitions occur can be phase-field type or at even larger scales yield macroscopic free boundary problems describing the evolution of phase interfaces. However, deterministic PDE models cannot always fully account for phase transition phenomena.

In the project iSTAMP, we aim at developing innovative stochastic dynamics and analysis suitable for a rigorous mathematical study of the effects of thermal fluctuations (“noise”).

Links:

• Hellenic Foundation for Research & Innovation

• FORTH: Institute of Applied & Computational Mathematics

• Department of Mathematics & Applied Mathematics, University of Crete