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原文連結
論文資訊
- 類型：已發表論文
- 日期：2012
摘要
The spectral bound, s(αA + βV), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in . Kato's result is shown here to imply, through an elementary “dual convexity” lemma, that s(αA + βV) is also convex in α > 0, and notably, ∂s(αA + βV)/∂α ≤ s(A). 擴散s typically haves(A) ≤ 0, so that for 擴散s with spatially heterogeneous growth or decay rates, greater mixing reduces growth. Models of the 演化 of dispersal in particular have found this result when A is a Laplacian or second-order elliptic operator, or a nonlocal 擴散 operator, implying selection for reduced dispersal. These cases are shown here to be part of a single, broadly general, “reduction” phenomenon.
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