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