The Solvability of Mixed Value Problem for the First and Second Approximations of One-Dimensional Nonlinear System of Moment Equations with Microscopic Boundary Conditions
Sakabekov A. Auzhani Y.
March 2022Atlantis Press
Journal of Nonlinear Mathematical Physics
2022#29Issue 1124 - 148 pp.
The paper gives a derivation of a new one-dimensional non-stationary nonlinear system of moment equations, that depend on the flight velocity and the surface temperature of an aircraft. Maxwell microscopic condition is approximated for the distribution function on moving boundary, when one fraction of molecules reflected from the surface specular and another fraction diffusely with Maxwell distribution. Moreover, macroscopic boundary conditions for the moment system of equations depend on evenness or oddness of approximation fk(t, x, c) , where fk(t, x, c) is partial expansion sum of the molecules distribution function over eigenfunctions of linearized collision operator around local Maxwell distribution. The formulation of initial and boundary value problem for the system of moment equations in the first and second approximations is described. Existence and uniqueness of the solution for the above-mentioned problem using macroscopic boundary conditions in the space of functions C([0 , T] ; L2[- a, a]) are proved.
Macroscopic boundary conditions , Maxwell microscopic condition , Nonlinear hyperbolic system of equations , System of moment equations
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Satbayev University, 22a Satpaev Str., Almaty, 050013, Kazakhstan
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