In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is th...

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...

We consider the Dirac equation in flat Minkowski 3–space and rewrite it as the Maxwell equation in Minkowski 4–space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to “negative frequencies”: we produce a real scalar invariant (charge) which indicates whether we are l...

Abstract. We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of [6, 7, 4], we propose a probabilistic interpretation of such a P.D.E. in terms of a nonlinear stochastic differential equation driven by a standard Brownian motion. We derive a numerical sch...

<p style='text-indent:20px;'>After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for PDEs describing dynamics fluid mixtures. While incompressible case with constant density was enlighted well enough due results Chen and Jüngel (isothermal case), or Marion Temam, some open questions remain solution ...

We investigate the interface dynamics in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation obtained by B.Shraiman and D.Bensimon, we derive intergro-differential evolution equation of interphase dynamics. It is shown that such representation of the conformal mapping technique is convenient for computer simulations of the quasi-stationary Stefan ...