Singular one-dimensional transport equations on L_p spaces

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• 作者：Chabi ; Mohamed ; Latrach ; Khalid
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2003
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：July 1, 2003
• 卷：283
• 期：1
• 页码：319-336
• 文件大小：157 K

摘要

We prove the well-posedness of the Cauchy problem governed by a linear mono-energetic singular transport equation (i.e., transport equation with unbounded collision frequency and unbounded collision operator) with specular reflecting and periodic boundary conditions on L_p spaces. The large time behaviour of its solution is also considered. We discuss the compactness properties of the second-order remainder term of the Dyson–Phillips expansion for a large class of singular collision operators. This allows us to evaluate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived.