Project-Team:IPSO

Project-Team Ipso

Members

Overall Objectives

Research Program

Application Domains

New Results

Multi-revolution composition methods for highly oscillatory differential equations
Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise
High order numerical approximation of the invariant measure of ergodic SDEs
PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
Weak second order explicit stabilized methods for stiff stochastic differential equations
Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field
A dynamic multi-scale model for transient radiative transfer calculations
Quasi-periodic solutions of the 2D Euler equation
Optimization and parallelization of Emedge3D on shared memory architecture
Vlasov on GPU (VOG Project)
Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus
Weak backward error analysis for overdamped Langevin equation
Weak backward error analysis for Langevin equation
Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme
An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
Asymptotic Preserving schemes for highly oscillatory Vlasov-Poisson equations
Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
On the controllability of quantum transport in an electronic nanostructure
The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties
Analysis of models for quantum transport of electrons in graphene layers
Analysis of a large number of Markov chains competing for transitions
Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems
Existence of densities for the 3D Navier–Stokes equations driven by Gaussian noise
Invariant measure of scalar first-order conservation laws with stochastic forcing
Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
Existence of densities for stable-like driven SDE's with Hölder continuous coefficients
Ergodicity results for the stochastic Navier-Stokes equations: an introduction
Weak truncation error estimates for elliptic PDEs with lognormal coefficients
Optimized high-order splitting methods for some classes of parabolic equations
Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds

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Bibliography

Inria | Raweb 2013 | Presentation of the Project-Team IPSO


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Section: New Results

Invariant measure of scalar first-order conservation laws with stochastic forcing

In [50] , we assume an hypothesis of non-degeneracy of the flux and study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by $L^{p}$ for some $p$ small, we are led to generalize to the stochastic case the theory of $L^{1}$ solutions developed by Chen and Perthame.

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