Diminishing functionals for nonclassical entropy solutions selected by kinetic relations

Diminishing Functionals for Nonclassical Entropy Solutions Selected by Kinetic Relations

We consider nonclassical entropy solutions to scalar conservation laws with concaveconvex flux functions, whose set of leftand right-hand admissible states ul, ur across undercompressive shocks is selected by a kinetic function ur = φ(ul). We introduce a new definition for the (generalized) strength of classical and nonclassical shocks, allowing us to propose a generalized notion of total varia...

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces, contrary to standard finite difference schemes. The main challenge is to achieve, at the discretization level, a consistency property with respect to a prescribed ...

Kinetic - energy functionals studied by surface calculations

Minimization of entropy functionals

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak constraint qualifications.

Statistical Inference for Rényi Entropy Functionals

Numerous entropy-type characteristics (functionals) generalizing Rényi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and distribution identification problems. We consider estimators of some entropy (integral) functionals for discrete and continuous distributions based on the numb...