ON THE EXISTENCE AND UNIQUENESS OF CLASSICAL SOLUTION FOR AN INITIAL-BOUNDARY VALUE PROBLEM FOR A DISCRETE BOLTZMANN SYSTEM IN TWO SPACE DIMENSIONS

The initial-boundary value problem for the two-dimensional regular four-velocity discrete boltzmann system is analyzed in a rectangle. The existence and uniqueness of classical global positive solution, bounded with its first partial derivatives are proved for a range of bounded data by the use of fixed points tools. A bound for the solution and its partial derivatives is provided.