An integro-PDE model with variable motility |
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| Affiliation: | 1. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 611756, People’s Republic of China;2. School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 611756, People’s Republic of China;1. Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 115 67 Praha 1, Czech Republic;2. Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Botswana International University of Science and Technology, Palapye, Botswana;3. Centro de Investigación en Creatividad y Educación Superior, Universidad de Santiago de Chile, Santiago, Chile;1. Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China;1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;2. College of Science, Henan University of Technology, Zhengzhou 450001, China;3. Henan Key Laboratory of Financial Engineering, Zhengzhou 450001, China |
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| Abstract: | This paper is concerned with a nonlocal reaction–diffusion–mutation model. It involves the spatial variable and a trait variable which govern the spatial diffusion of species. By establishing comparison principle and constructing monotone iterative sequence, we have proved the existence of solution to Cauchy problem. Then, based on the quasi-elementary solution, auxiliary equation and method of successive improvement of upper and lower solutions, the solutions are shown to be unique, bounded and globally stable. |
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| Keywords: | Nonlocal Reaction–diffusion equation Mutation Mathematical ecology |
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