The " Newtonian " theory of spatially unbounded, self–gravitating, pres-sureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space...

Khokhlov–Zabolotskaya–Kuznetsov equation (φt + φφx − αφxx)x − 1/2(φyy + φzz) = 0 and its solutions are analyzed. A series of complete exact analytical solutions related to the one-dimensional and vectorial inhomogeneous Burgers equation are presented. A concrete example which corresponds to a special form of the inhomogeneous term is analyzed. Reduction to the traveling wave solution is conside...

We investigate kinetic models of a system in contact with several spatially homogeneous thermal reservoirs at different temperatures. We explicitly find all spatially homogeneous non-equilibrium stationary states (NESS). We then consider the question of whether there are also non spatially uniform NESS. This remains partly open in general, except for a class of models to which we can apply prob...

Abstract We conclude the classification of cohomogeneity one actions on symmetric spaces rank by classifying quaternionic hyperbolic up to orbit equivalence. As a by-product our proof, we produce uncountably many examples inhomogeneous isoparametric families hypersurfaces with constant principal curvatures in spaces.

We use WZ-summation methods to compute recurrences for the Ising-class integrals Cn,k. In this context, we describe an algorithmic approach to obtain homogeneous and inhomogeneous recurrences for a general class of multiple contour integrals of Barnes’ type.