Related papers: Uncertainty Quantification for Linear Hyperbolic E…
We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…
We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others describing…
In this paper, by means of the Gronwall inequality, the {\psi}-Riemann-Liouville fractional partial integral and the {\psi}-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these…
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grad's moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the…
In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
In this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients. This means to assume that the coefficients are less regular than H\"older. The characteristic roots are also allowed to have…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where…
In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…
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…
The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns…
Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…