Robust optimization Ensemble forecasting White noise Conduction Regularity Helmholtz decomposition Lower-bound gradient estimate Fine-scale substructure Nonlocal Hamilton-Jacobi Equations Highly oscillatory problems Asymptotic analysis Nonlinear Schrödinger equation Navier-Stokes Equations Boundary layer Stroboscopic averaging Degenerate parabolic equations Formal series Modal analysis Oceanography Timoshenko beam Stability Backward error analysis Conservation laws Entropy DATA ASSIMILATION Viscosity solutions Adjoint model Fluid mechanics Highly-oscillatory FOS Mathematics Nonlocal front propagation Diffusion limit Scattering Large eddy simulation Uncertainty quantification Maximum principle Two-scale convergence Stochastic partial differential equations Numerical simulations Optimization Asymptotic Analysis Fluid-structure interaction Hamilton-Jacobi equations Elasticity Uniform accuracy Asymptotic preserving schemes Turbulence models Reaction-diffusion system Averaging MPCC 65L20 Reaction-diffusion Density matrix Finite element method Dislocation dynamics Vlasov-Poisson equation Global existence Long-time behavior Level-set approach Dynamical system Robust control Homogenization Asymptotic behavior Population dynamics Invariant measure BGK equation Convergence Numerical simulation Subdivision Spectral set Cardiac electrophysiology Micro-macro decomposition PIV Porous media Optimal control Vlasov equation Concrete Kinetic equations B-series Data assimilation Fractured porous media $L^1-$dependence in time Finite Element Method Chapman-Enskog expansion Interaction fluide-structure Shape optimization Ensemble forecasts Numerical range Controllability Diffusion Deconvolution models Navier-Stokes equations Schrödinger equation Markov chain Binary alloys Finite elements Interpolation Eikonal equation Turbulence Error estimate