In this article the numerical approximation of the stochastic transport equation is considered. We propose a new computational scheme for the effective simulation of the solutions of this equation. Results on the convergence ...

We study random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the ...

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is an obstacle type equation, min{−1 ∞u(x), (u − v)(x)} = 0, and the second one is −v(x) + v(x) − u(x) = h(x) in a ...

In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the ...

We present OpenMP versions of C and Fortran programs for solving the Gross–Pitaevskii equation for a rotating trapped Bose–Einstein condensate (BEC) in two (2D) and three (3D) spatial dimensions. The programs can be used ...