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