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In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed…
This paper studies the long time stability of both stochastic heat equations on a bounded domain driven by a correlated noise and their approximations. It is popular for researchers to prove the intermittency of the solution which means…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
We provide sufficient conditions for the existence of invariant probability measures for generic stochastic differential equations with finite time delay. This is achieved by means of the Krylov-Bogoliubov method. Furthermore, we focus on…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Simultaneous measurements of position and momentum are considered in $n$ dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…
We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…