Cauchy problem Apparent diffusion coefficient Multiscale modeling Prion Hematopoietic stem cells Dynamics Shallow water equations Error bounds Numerical simulations Navier-Stokes system Diffusion limit Cell dynamics Product integration method Bergman kernel HWI inequality Kinetic equation Fredholm integral equation Viscoelasticity Asymptotic expansion Stability Mixed finite elements Geophysical fluid dynamics Euler characteristic Diffusion encoding gradient Contact problem Harmonic limit Variational inequality Energy conservation Asymptotic analysis Chronotherapy Diffusion magnetic resonance imaging Hamiltonian dynamics Differential equations Coulomb friction Blood coagulation Elastodynamics Linear elasticity Elasticity Cross diffusion Finite elements Finite element method Kinetic equations Hopf bifurcation Bloch-Torrey equation Flow convexity Prions Cancer Abbreviated action integral Fracture propagation Agent-based models Alzheimer History-dependent boundary condition Asymptotic convergence Nitsche's method Amplitude equation Partial differential equations Cell cycle Cellular differentiation Tresca’s friction law Plasma physics Solvability conditions Kinetic formulation Energy dissipation Anti-diffusive method Finite element Cell population dynamics 92C37 Hele-Shaw Finite volumes Circadian clock Age-structured PDE Hematopoiesis Stochastic partial differential equations Clot growth Spectral stability Fixed-stress iterative coupling Data completion Biot system Delay differential-difference system Existence of pulses Stokes equations Compressible flows Dynamical core Unilateral contact Transport equations Entropy method Navier-Stokes equations Blow-up Homogenization Entropy Convergence Traveling wave Immune response Dispersion relationship Traveling waves Cardiac diffusion imaging Delay differential equations Contact Finite volume scheme Mass redistribution method