在线阅读 --自然科学版 2020年2期《一类刻画沿海含水层系统的二阶抛物方程组边值问题解析解的存在唯一性》
一类刻画沿海含水层系统的二阶抛物方程组边值问题解析解的存在唯一性--[在线阅读]
于飞, 蒋鹏, 郭巧娜
河海大学 理学院, 江苏 南京 210098
起止页码: 93--99页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.02.001
摘要
为了求解一类二阶抛物型方程组边值问题解的存在唯一性,刻画了在潮汐与内陆补给的共同影响下,由半透水层和延伸至海底的承压含水层组成的沿海含水层体系.利用复空间中的分离变量法,求出了此方程组的显式解析解.同时,利用反证法证明了此解析解是唯一的.

The Existence and Uniqueness of Analytical Solutions to Boundary Value Problems for a Class of Second-order Parabolic Systems Characterizing Coastal Aquifer Systems
YU Fei, JIANG Peng, GUO Qiaona
College of Science, Hohai University, Jiangsu Nanjing 210098, China
Abstract:
The purpose of this paper is to solve the existence and uniqueness of solutions to boundary value problems for a class of second-order parabolic systems.The system characterizes the coastal aquifer system consisting of a semipermeable layer and a confined aquifer extending to bottom of the sea,under the influence of tide and inland supplies.This paper mainly use the method of separation of variables in the complex space to get the explicit analytical solutions of the system.At the same time,we prove the uniqueness of this analytical solution by contradiction.

收稿日期: 2019-10-10
基金项目: 江苏省自然科学基金(BK20191296);中央高校业务费(2019B19114)

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