Abstract We provide a rigorous mathematical framework to establish the hydrodynamic limit of Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by order describe phase transition fluids kinetic equations. prove that, when scale parameter tends 0, this converges nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms...

this study was carried out to obtain quantitative relationships between zn in equilibrium solution and that retained by 20 calcareous soils. soils were brought into equilibrium with varying solution concentrations of zn, and the amounts removed from solution were used to check the fit to six adsorption isotherms, namely, freundlich, langmuir, temkin, gunary, two surface langmuir and adjusted fr...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...