Solving Boltzmann Equation, Part I: Green’s Function

We present an approach for solving the Boltzmann equation based on the explicit construction of the Green’s functions. The Green’s function approach has been useful for the study of nonlinear interior waves and the boundary waves. In this Part I we study the Green’s functions for the initial and initial-boundary value problems. In the forthcoming Part II, we will study the general solutions of the Boltzmann equation. Our presentation is self-contained, and, besides the synthesis of the existing ideas, we also established the detailed analysis of the leading terms of the Green’s function.