The Heat Equation is one of the three classical linear partial differential equations of second
order that form the basis of any elementary introduction to the area of PDEs, and only …

We present a new formulation of multidimensional scalar conservation laws, which includes
both the equation and the entropy criterion. This formulation is a kinetic one involving an …

Using relative entropy estimates about an absolute Maxwellian, it is shown that any properly
scaled sequence of DiPerna‐Lions renormalized solutions of some classical Boltzmann …

This book gives a general presentation of the mathematical and numerical connections
kinetic theory and conservation laws based on several earlier works with PL Lions and E …

We present an existence and a stability proof for solutions to the BGK model of Boltzmann
Equation δ, f+ v·▽ x f+ f= M [f], t⩽ 0, x∈ RN, v∈ RNM [f]=(p (2φT) N 2) exp (−| v− u| 2 2T),(p …

In the modern theory of boundary value problems the following ap proach to investigation is
agreed upon (we call it the functional approach): some functional spaces are chosen; the …

We complete the theory of velocity averaging lemmas for transport equations by studying the
limiting case of a full space derivative in the source term. Although the compactness of …

Since the nineteenth century, when Boltzmann formalized the concepts of kinetic equations,
their range of application has been considerably extended. First introduced as a means to …

The classical models of fluid dynamics, such as the Euler or Navier–Stokes equations, were
first established by applying Newton's second law of motion to each infinitesimal volume …

In this paper the stability of the Vlasov–Poisson–Fokker–Planck with respect to the variation
of its constant parameters, the scaled thermal velocity and the scaled thermal mean free …