V. D. Gordevskii, A. A. Gukalov
Maxwell distributions in a model of rough spheres //
Ukrainian Mathematical Journal ,
Vol. 63, No. 5, pp. 629–639,
We consider the Boltzmann equation for the model of rough spherical molecules with both translational and rotational energies. The general form of local Maxwellian distributions for this model is obtained. The main possible types of the corresponding gas flows are selected and analyzed.
Keywords: Angular Velocity,Boltzmann Equation, Kinetic Theory, Maxwell Distribution, Solid Sphere
V.D.Gordevskyy, A.A.Gukalov
Interaction of the eddy flows in the Bryan-Pidduck model //
Visnyk of Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics,
2011, v. 990, p.27-41.,
The interaction between the two eddy streams of a gas of rough spheres is investigated. A bimodal distribution with a Maxwellian modes of a special form is used. Different sufficient conditions for the minimization of the uniform-integral discrepancy between the sides of the equation Bryan-Piddaсk is obtained.
A.A. Gukalov
Interaction between "Accelerating-Packing" Flows for the Bryan-Pidduck Model //
Journal of Mathematical Physics, Analysis, Geometry,
vol. 9, No 3, pp. 316-331 ,
The interaction between the "accelerating-packing" flows in a gas of rough spheres is studied. A bimodal distribution with the Maxwellian modes of special forms is used. Different sufficient conditions for the minimization of the uniform-integral error between the sides of the Bryan-Pidduk equation are obtained.
Keywords: rough spheres, Bryan-Piddack equation, Maxwellian, "acce- lerating-packing" flows, error, bimodal distribution.
Gordevskii, V.D., Gukalov, A.A.
Interaction of locally Maxwellian flows in the model of rough spheres. //
Theoretical and Mathematical Physics,
176, 1100–1113 (2013). ,
We construct new approximate explicit solutions of the nonlinear kinetic Bryan-Pidduck equation. They have the form of linear combinations of two local Maxwellians of the “accelerating-packing” type and minimize the uniform-integral weighted residual between the sides of the equation.
Keywords: Bryan-Pidduck equation, approximate explicit solution, accelerating packing,weighted residual
O. O. Hukalov, V. D. Gordevskyy
Infinite-modal approximate solutions of the Bryan-Pidduck equation //
Matematychni Studii,
vol. 49, No 1, pp. 95-108,
The nonlinear integro-differential Bryan-Pidduck equation for a model of rough spheres is considered. An approximate solution is constructed in the form of an infinite linear combination of some Maxwellian modes with coefficient functions that depend on time and spatial coordinate. Sufficient conditions for the infinitesimality of the uniformly-integral error between the parts of the Bryan-Pidduck equation are obtained.
Keywords: Bryan-Pidduck equation; rough spheres; uniform-integral error; infinite-modal approximate solutions; global Maxwellian; screws
O.O.Hukalov, V.D.Gordevskyy
The Interaction of the Maxwell Flows of General Form for the Bryan-Pidduck Model //
Journal of Mathematical Physics, Analysis, Geometry,
2018, vol. 14, No 1, pp. 54-66,
The interaction between the two Maxwell flows of general form in a gas of rough spheres is studied. The approximate solution of the Bryan–Pidduck equation describing the interaction is a bimodal distribution with specially selected coefficient functions. It is shown that under certain additional conditions imposed on these functions and hydrodynamic parameters of the flows, the norm of the difference between the parts of the Bryan–Pidduck equation can be arbitrarily small.
Keywords: rough spheres, Bryan–Pidduck equation, error, Maxwellian flows, bimodal distribution, hydrodynamic parameters.
