in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this paper we shall establish a result concerning the covering dimension of a set of the type {x ∈ X : Φ(x)∩Ψ(x) 6= ∅}, where Φ, Ψ are two multifunctions from X into Y and X, Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a descript...

Path-dependent impulse differential inclusions, and in particular, path-dependent hybrid control systems, are defined by a path-dependent differential inclusion (or path-dependent control system, or differential inclusion and control systems with memory) and a pathdependent reset map. In this paper, we characterize the viability property of a closed subset of paths under an impulse path-depende...

In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which we call Bregman ISS and Linearized Bregman ISS. We show that under proper conditions, there exists a bias-free and sign-consistent point on their solution paths, which corresponds to a signal that is the unbiased estimate of the true signal and whose entries have the...

Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not ne...

In the paper, we study weak invariance of differential inclusions with non-fixed time impulses under compactness type assumptions. When the right-hand side is one sided Lipschitz an extension of the well known relaxation theorem is proved. In this case also necessary and sufficient condition for strong invariance of upper semi continuous systems are obtained. Some properties of the solution set...