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Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are…
We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from…
A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…
In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies for nonautonomous…
In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm…
We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may…
We consider a system of nonlinear equations which can be reduced to a degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary conditions for the existence of a weakly singular solution of heat wave type…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…