Homogenization for semilinear hyperbolic systems with oscillatory data
Thomas Y. Hou · Communications on Pure and Applied Mathematics · 1988
Abstract The behavior of multi‐dimensional discrete Boltzmann systems with highly oscillatory data is studied. Homogenized equations for the mean solutions are obtained. Uniform convergence of the oscillatory solutions of the discrete Boltzmann equations to the solutions of the corresponding homogenized equations is established. Moreover, we find that the weak limits of the oscillatory solutions for a model of Broadwell type are not continuous functions of the discrete velocities. Generalization of the above results to problems with multiple‐scale initial data is also established.