GLOBAL C~(1,2)-SOLUTION TO FUNCTIONAL REACTION-DIFFUSION PROBLEM

• 作者: Guangshan Xu Zhongtai Ma
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: existence and UNIQUENESS FUNCTIONAL REACTION-DIFFUSION problem Schau-der fixed point theorem MONOTONE ITERATION method SUPPER and lower solutions
• 年，卷（期）: 2013,（2）
• 页码范围: 230-237
• 页数: 8页
• 分类号: O175

摘要

This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is derived using Schauder fixed point theorem in Banach space instead of the Ascoli-Arzela theorem in the unbounded region, meanwhile, the maximal and minimal solutions are also presented by the monotone iteration method with a pair of supper and lower solutions as the initial iteration.