We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L(H ; ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under bo...

We present a new dispersive analysis of the isospin breaking decay η → 3π. The resulting representation of the decay amplitude allows us to determine the quark mass double ratio Q and we find as a preliminary result Q = 22.3 ± 0.4. Finally, we discuss a number of improvements that we intend to implement in the future.

The purpose of the present paper is to establish the local energy decay estimates and dispersive estimates for 3-dimensional wave equation with a potential to the initial-boundary value problem on exterior domains. The geometrical assumptions on domains are rather general, for example non-trapping condition is not imposed in the local energy decay result. As a by-product, Strichartz estimates i...

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SMARTMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correc...