Existence and Uniqueness Theorems for the Nonlinear Boltzmann Equation

  • Abdigali Shoynbayuly Akysh


In 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