Related papers: Scalar conservation laws with stochastic discontin…

This paper deals with an optimal control problem and describes the reachable set for the scalar 1-D conservation laws with discontinuous flux. Regarding the optimal control problem we first prove the existence of a minimizer and then we…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation…

We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator ${\mathcal L}_x$ for which we…

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by…

Here we consider scalar conservation law in one space dimension with strictly convex flux. Goal of this paper is to study two problems. First problem is to know the profile of the entropy solution. In spite of the fact that, this was…

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…

This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…

The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

Self-similarity of Burgers' equation with some stochastic advection is studied. In self-similar variables a stationary solution is constructed which establishes the existence of a stochastically self-similar solution for the stochastic…

We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random…

We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…

We study nonlinear hyperbolic conservation laws posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable), a class of…

A stochastic and variational aspect of the Lax-Friedrichs scheme was applied to hyperbolic scalar conservation laws by Soga [arXiv: 1205.2167v1]. The results for the Lax-Friedrichs scheme are extended here to show its time-global stability,…

We consider self-similar solutions describing intermittent bursts in shell models of turbulence, and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to…

In spite of many attempts to model dense granular flow, there is still no general theory capable of describing different types of flows, such as gravity-driven drainage in silos and wall-driven shear flows in Couette cells. Here, we…

We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…

Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…

Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyperbolicity of the underlying hyperbolic system. We apply a…