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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (7): 45-57.doi: 10.6040/j.issn.1671-9352.0.2024.339

• 生物数学 • 上一篇    

随机交叉扩散种群-毒物模型鞅解的存在性

杜艳艳,王宗*   

  1. 青岛理工大学理学院, 山东 青岛 266520
  • 发布日期:2026-07-01
  • 通讯作者: 王宗(1995— ),男,讲师,博士,研究方向为随机种群动力学. E-mail:wangzong95@163.com
  • 作者简介:杜艳艳(1994— ),女,讲师,博士,研究方向为随机种群动力学. E-mail:mduyanyan@163.com *通信作者:王宗(1995— ),男,讲师,博士,研究方向为随机种群动力学. E-mail:wangzong95@163.com

Existence of martingale solution to stochastic cross-diffusion population-toxicant model

DU Yanyan, WANG Zong*   

  1. School of Science, Qingdao University of Technology, Qingdao 266520, Shandong, China
  • Published:2026-07-01

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摘要： 建立具有交叉扩散的随机种群-毒物模型;利用Galerkin有限元逼近方法,得到随机交叉扩散模型在有限维空间中的近似解;通过分析近似解的存在唯一性、胎紧性及弱收敛性, 证明该模型在Hilbert空间全局鞅解的存在性。

关键词: 种群-毒物模型, 鞅解, 伽辽金近似, 交叉扩散

Abstract: In this paper, a random population-toxicant model with cross diffusion is established, and the approximate solution of the random cross diffusion model in finite dimensional space is obtained by using Galerkin finite element approximation method. The existence of the martingale solution in Hilbert space is proved by analyzing the existence and uniqueness, tightness criterion and weak convergence of the approximate solution.

Key words: population-toxicant model, martingale solutions, Galerkin approximation, cross diffusion

中图分类号: 

  • O175
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