Cauchy problem for the Fokker–Planck–Kolmogorov equation of a multidimensional normal Markovian process

We present the results of studying the fundamental solution and correct solvability of the Cauchy problem as well as the integral representation of solutions for the Fokker–Planck–Kolmogorov equation of a class of normal Markovian processes.     

On the Cauchy Problem for $$\mathop {2b}\limits^ \to$$ -Parabolic Systems with Growing Coefficients

For -parabolic dissipative systems and systems with growing coefficients as |x| in the presence of degeneracies in the initial hyperplane, we investigate the fundamental matrix of solutions and the solvability of the Cauchy problem.     

Simulating van der Waals interactions in water/hydrocarbon-based complex fluids

In systems composed of water and hydrocarbons, Van der Waals interactions are dominated by the nonretarded, classical (Keesom) part of the Lifshitz interaction; the interaction is screened by salt and extends over mesoscopic distances of the order of the size of the (micellar) constituents of complex fluids. We show that these interactions are included intrinsically in a recently introduced local Monte Carlo algorithm for simulating electrostatic interactions between charges in the presence of nonhomogeneous dielectric media.