We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) â‰¥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = âˆ†vm where m > 1 is aâ€¦ (More)

A class of numerical schemes for nonlinear kinetic equations of Boltzmann type is described. Following Wildâ€™s approach, the solution is represented as a power series with parameter dependingâ€¦ (More)

We introduce and discuss certain kinetic models of (continuous) opinion formation involving both exchange of opinion between individual agents and diffusion of information. We show conditions whichâ€¦ (More)

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble ofâ€¦ (More)

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut = âˆ’(uuxxx)x , modeling the evolution of the interface ofâ€¦ (More)

We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with conÂ®nement by a uniformly convex potential, 2) unconÂ®ned scalarâ€¦ (More)

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary statesâ€¦ (More)

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting withâ€¦ (More)

Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diiusive scaling that leads to the diiusion equations. In manyâ€¦ (More)