Abstract linear partial differential equations related to size-structured population models with diffusion
Abstract linear partial differential equations related to size-structured population models with diffusion
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DOI：
10.1016/j.jmaa.2015.11.077
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发表时间：
2016-04
影响因子：
1.3
通讯作者：
N. Kato
中科院分区：
文献类型：
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作者：
N. Kato
我们研究巴拿赫空间和/或巴拿赫格子中的抽象线性偏微分方程，这些方程与具有空间扩散的规模结构人口模型及其对偶问题有关。我们通过半群理论和特征方法引入温和解并研究温和解的可微性。显示了独特的温和溶液的存在。此外，还获得了比较结果，并研究了 Banach 晶格设置中温和解的有界性。此外，我们考虑对偶问题，然后引入弱解并确定它们的唯一性。
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.