中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (4): 28-31.

• 研究论文 • 上一篇    下一篇

一个二维纯林发展系统的古典解

徐龙封,吴 慧
  

  1. (安徽工业大学数理学院,安徽 马鞍山 243002)
  • 收稿日期:2010-07-28 修回日期:1900-01-01 出版日期:2011-07-25 发布日期:2011-07-25

Classical Solution of a TwoDimensional Dynamics System for Pure Forest

XU Longfeng,WU Hui

  

  1. (School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China)
  • Received:2010-07-28 Revised:1900-01-01 Online:2011-07-25 Published:2011-07-25

摘要: 二维森林发展系统模型的研究还未见到任何结果。针对这类系统初始状态依赖于林木总量,而边界状态又依赖于初始状态,系统的边界不满足通常的三类条件之一的特点,采用在“树龄-直径”存在区域内引进一类特殊的曲线族,避开了提边界条件问题。再利用适当地选择林木直径尺度量纲的技巧,提出了一个适定的二维纯林发展系统模型,最后综合拉特征线、先验估计、构造初始状态积分方程、迭代等技巧证明了这个系统整体古典解的存在唯一性。

关键词: 二维系统, 特征线, 古典解, 积分方程

Abstract: The research of two-dimensional forest dynamics system model is still open.First, for the peculiarity of two-dimensional forest dynamics systems with initial state depending only on total quantity of forest, and boundary condition depending only on initial state again, boundary of system not satisfying one of 3 kinds common conditions, by introducing a class of special family curves in presence region of “stand agediameter”, the problem of boundary conditions is avoided. Secondly, using the technique of selecting measure dimension of lumber diameter properly, a wellposed two-dimensional forest dynamics system model is propounded. At last, colligating the technique of pulling characteristic curve, a prior -estimate, structuring integral equation of initial state, iteration, the existence and uniqueness of the global classical solution are proved for this system.

Key words: two-dimensional systems, characteristic line, classical solution, integral equation

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