On the initial boundary value problems for the Enskog equation in irregular domains
type: Item
instance of: scholarly article
title: On the initial boundary value problems for the Enskog equation in irregular domains
zbMATH Open document ID: 0921.45006
DOI: 10.1023/A:1023268718526
author: K. Appert
published in: Journal of Statistical Physics
publication date: 1999-09-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 1279371
zbMATH Keywords: Enskog equation
zbMATH Keywords: \(H\)-theorem
zbMATH Keywords: irregular domains
zbMATH Keywords: initial boundary value problems
zbMATH Keywords: cone condition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1279371