Motivated by the recent investigation of a predator-prey model in heterogeneous environments [20], we show that the maximum of the unique positive solution of the scalar equation {mu Delta theta + (m(x) - theta)theta = 0 in Omega, partial derivative theta/partial derivative n = 0 on partial derivative Omega (0,1) is a strictly monotone decreasing function of the diffusion rate it for several classes of function m, which substantially improves a result in [20]. However, the minimum of the positive solution of (0.1) is not always monotone increasing in the diffusion rate [15].
机构:
Northwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
Bai, Xueli
He, Xiaoqing
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E China Normal Univ, Ctr PDE, 500 Dongchuan Rd, Shanghai 200241, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
He, Xiaoqing
Li, Fang
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E China Normal Univ, Ctr PDE, 500 Dongchuan Rd, Shanghai 200241, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
机构:
East China Normal Univ, Ctr Partial Differential Equat, Shanghai 200241, Peoples R China
Univ Minnesota, Sch Math, Minneapolis, MN 55455 USAUniv Miami, Dept Biol, Coral Gables, FL 33124 USA
机构:
Northwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
Bai, Xueli
He, Xiaoqing
论文数: 0引用数: 0
h-index: 0
机构:
E China Normal Univ, Ctr PDE, 500 Dongchuan Rd, Shanghai 200241, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
He, Xiaoqing
Li, Fang
论文数: 0引用数: 0
h-index: 0
机构:
E China Normal Univ, Ctr PDE, 500 Dongchuan Rd, Shanghai 200241, Peoples R ChinaNorthwestern Polytech Univ, Dept Appl Math, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China
机构:
East China Normal Univ, Ctr Partial Differential Equat, Shanghai 200241, Peoples R China
Univ Minnesota, Sch Math, Minneapolis, MN 55455 USAUniv Miami, Dept Biol, Coral Gables, FL 33124 USA