Existence and Uniqueness Theorems for the Nonlinear Boltzmann Equation
AbstractIn this paper, based on the scheme of the splitting method, the existence and uniqueness theorems are proved in the global in time t ∈ [0, T], T < ∞ for the complete nonlinear Boltzmann equation in non-equilibrium case, when intermolecular interactions are the molecules-hard spheres and the central forces. Based on existence-bounded solution in the space C, the study proves a strict positivity of the solution to the complete nonlinear Boltzmann equation, when the initial function is positive. Based on this, some mathematical justification of Boltzmann's H-theorem is presented.Keywords: Complete nonlinear Boltzmann equation, splitting method, existence and uniqueness theorem, positivity of the solution of the nonlinear Boltzmann equation, H-Boltzmann theorem
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