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