in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for velocity average of solutions kinetic equations. This requires only elementary techniques in Fourier analysis and shows new range assumptions that are sufficient be $L^2([0,T],H^{1/2}_x).$ result not an interesting connection between lemmas local smoothing property dispersive equations, but ...

Quantitative analysis of fast and slow diffusion from abdominal Diffusion-weighted MRI has the potential to provide important new insights into physiological and microstructural properties of the body. However, the commonly used, independent voxel-wise fitting of the signal decay model leads to imprecise parameter estimates, which has hampered their practical usage. In this work we evaluated th...

Introduction. Whitham's averaged equations [1] for a nonlinear evolution system describe slow modulations of parameters on a family of periodic traveling wave solutions (or on families of multiphase quasiperiodic solutions, which are so far knows to exist only for integrable equations) and are a system of hydrodynamic type [2, 3], that is, of the form