The Convergence of a Class of Quasimonotone Reaction-Diffusion Systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Convergence of a Class of Quasimonotone Reaction-Diffusion Systems

Authors:	Wang Yi; Jiang Jifa

Institution:	Department of Mathematics, University of Science and Technology of China Hefei, Anhui 230026, China, wangyi{at}mail.ustc.edu.cn Department of Mathematics, University of Science and Technology of China Hefei, Anhui 230026, China, jiangjf{at}ustc.edu.cn

Abstract:	It is proved that every solution of the Neumann initial-boundaryproblem converges to some equilibrium, if the system satisfies (i) ${partial}$ F_i/ ${partial}$ u_j $≥$ 0 for all 1 $≤$ i $!=$ j $≤$ n, (ii) F(u * g(s)) $≥$ h(s) * F(u) wheneveru $isin$ and 0 $≤$ s $≤$ 1, where x *y = (x₁y₁, ..., x_ny_n) and g, h : 0, 1] $->$ 0, 1]ⁿ are continuousfunctions satisfying g_i(0) = h_i(0) = 0, g_i(1) = h_i(1) = 1, 0< g_i(s); h_i(s) < 1 for all s $isin$ (0, 1) and i = 1, 2, ...,n, and (iii) the solution of the corresponding ordinary differentialequation system is bounded in . We also study the convergence of the solution of the Lotka–Volterrasystem where r_i > 0, ${alpha}$ $≥$ 0, and a_ij $≥$ 0 for i $!=$ j.

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