On the initial boundary value problems for the Enskog equation in irregular domains
The existence and uniqueness of the solution of the Enskog equation in bounded spatial domains is proved for large initial \(L^1\)-data. The boundary of the spatial domain (in \({\mathbb R}^n\)) is only assumed to have finite \((n-1)\)-dimensional Hausdorff measure and to satisfy a cone condition. The boundary reflection operator is assumed linear, positive, local in position, and satisfying a certain upper bound. The existence and uniqueness is first established for the corresponding Enskog equation with bounded velocities. Then, using estimates for certain higher velocity moments, the result is extended to Enskog equations with unbounded velocities. An \(H\)-theorem is proved as well.
scientific article; zbMATH DE number 1279371