Stochastic Galerkin methods have become a significant tool for the resolution of stochastic partial differential equations (SPDE). However, they suffer from prohibitive computational times and memory requirements when dealing with large scale applications and high stochastic dimensionality. Some alternative techniques, based on the construction of suitable reduced deterministic or stochastic ba...

Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of this equation. Bertini, Cancrini and Giacomin [2, 3] have proposed a notion of a solution through a limiting procedure and a certain renormalization of the ...

This survey critically discusses high-concentration-capacity (HCC) headspace (HS) techniques applied to sample the volatile fraction of matrices of interest in the flavors and fragrance fields. In particular, the advantages, limits, and fields of application of HS solid-phase microextraction (SPME), high-capacity HS sorptive extraction (HSSE) and HS solid-phase dynamic extraction (SPDE) are eva...

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L1 setting requiring no growth assumptions on the nonline...

with a highly irregular function F (t, x), as well as nonlinear versions of these equations. However, if F is ”very rough” then, presumably, the solution u(t, x) will not be very smooth either, hence one would not be able to differentiate it in time or space, and the sense in which u(t, x) solves the corresponding equation is not quite clear. It is natural to think of u(t, x) as a weak solution...

In this survey we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization and singular PDEs, their mean limit problems. particular discuss the O(N) linear sigma model two three dimensional torus. The procedure leads to a coupled system of interacting $\Phi^4$ equations. d = 2, show uniform bounds for dynamics convergence mean-field SPDE. For enou...