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