Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614412 | Journal of Mathematical Analysis and Applications | 2016 | 21 Pages |
Abstract
We study abstract linear partial differential equations in Banach spaces and/or Banach lattices related to size-structured population models with spatial diffusion and their dual problems. We introduce mild solutions through semigroup theory and characteristic method and investigate differentiability of mild solutions. Existence of a unique mild solution is shown. Also, a comparison result is obtained as well as the boundedness of mild solutions is investigated in the Banach lattice setting. Furthermore, we consider the dual problems, and then we introduce weak solutions and establish their uniqueness.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Nobuyuki Kato,