High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require positivity of thermodynamic quantities in order to guarantee their well-posedness. In this work, we introduce a limiting strategy discretizations constructed by blending high solutions with low positivity-preserving discretization. The proposed discretization is semi-discretel...

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.

We show that any Hermiticity and trace preserving continuous semigroup {γt}t>0 in d dimensions is completely positive if and only if the semigroup {γt⊗ γt}t>0 is positivity preserving.

Complete characterization of complete positivity preserving nonMarkovian master equations is presented.