Martingale solutions of stochastic nonlocal cross-diffusion systems

Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Numerical fluid solutions for nonlocal electron transport in hot plasmas: Equivalent diffusion versus nonlocal source

Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion sol...

Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Solutions of diffusion equation for point defects

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...

Equivalence of stochastic equations and martingale problems

The fact that the solution of a martingale problem for a diffusion process gives a weak solution of the corresponding Itô equation is well-known since the original work of Stroock and Varadhan. The result is typically proved by constructing the driving Brownian motion from the solution of the martingale problem and perhaps an auxiliary Brownian motion. This constructive approach is much more ch...