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Differential Equations

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Differential Equations

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Research Frontiers in Stochastic Partial Differential Equations

Mathematical treatment of PDEs with random coefficients and noise using functional analysis and measure-theoretic probability.

Noise-Induced Pattern Formation in Reaction-Diffusion Systems
Stochastic Blow-Up and Finite-Time Singularities
Multiscale Homogenization in Random Media
Pathwise Regularity and Rough Path Theory
Long-Time Asymptotics in Stochastic Evolution Equations
Coupling Methods for Nonlinear SPDEs
Rare Events and Large Deviations in Fluids
Regularity Structures Beyond Polynomial Chaos
Ergodicity and Mixing in Non-Reversible Systems
Dimensional Reduction in High-Dimensional Stochastic Dynamics

All Differential Equations PhD categories