Observation estimate for kinetic transport equations by diffusion approximation

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

Fractional diffusion limit for collisional kinetic equations

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite v...

Approximation of Transport Equations by Matrix Equations and Sequential Sampling

Observability Estimate and State Observation Problems for Stochastic Hyperbolic Equations

In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique cont...

Generalized phase-space kinetic and diffusion equations for classical and dispersive transport

We formulate and solve a physically-based, phase space kinetic equation for transport in the presence of trapping. Trapping is incorporated through a waiting time distribution function. From the phase-space analysis, we obtain a generalized diffusion equation in configuration space. We analyse the impact of the waiting time distribution, and give examples that lead to dispersive or nondispersiv...