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- W2890908170 abstract "Motivated by the recent investigation of a predator-prey model in heterogeneous environments cite{LouYuan-WangBiao}, we show that the maximum of the unique positive solution of the scalar equation begin{equation}label{eq:01}begin{cases} muDeltatheta+(m(x)-theta)theta=0 hspace{0.5em} &text{in}hspace{0.5em}Omega, frac{partial theta}{partial n}=0 hspace{0.5em} &text{on}hspace{0.5em}partialOmega end{cases}end{equation} is a strictly monotone decreasing function of the diffusion rate $mu$ for several classes of function $m$, which substantially improves a result in cite{LouYuan-WangBiao}. However, the minimum of the positive solution of eqref{eq:01} is monotone increasing under proper assumptions on the resource function, it is not always monotone increasing in the diffusion rate cite{HeXiaoqing-NiWeiMing2016}." @default.
- W2890908170 created "2018-09-27" @default.
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- W2890908170 date "2018-09-17" @default.
- W2890908170 modified "2023-09-23" @default.
- W2890908170 title "Some monotone properties for solutions to a reaction-diffusion model" @default.
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- W2890908170 doi "https://doi.org/10.48550/arxiv.1809.06519" @default.
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