一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题

J4 ›› 2010, Vol. 45 ›› Issue (6): 70-73.

一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题

王娟¹,刘辉昭²

1. 内蒙古科技大学数理与生物工程学院, 内蒙古包头 014010;
2. 河北工业大学理学院, 天津 300130

收稿日期:2009-08-18 出版日期:2010-06-16 发布日期:2010-06-17
作者简介:王娟 (1981-),女,硕士,讲师,研究方向为偏微分方程的理论及应用.Email:tlwangjuan@yahoo.com.cn

The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equations

WANG Juan¹, LIU Hui-zhao²

1. School of Mathematics,Physics and Biological Engineering,Inner Mongolia University of Science and Technology,
Baotou 014010, Inner Mongolia,China; 2. School of Sciences, Hebei University of Technology,
Tianjin 300130, China

Received:2009-08-18 Online:2010-06-16 Published:2010-06-17

摘要/Abstract

摘要：

证明了一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题的古典解的存在惟一性。用比较原理证明了该问题至多存在一个古典解。在一定条件下,通过构造辅助函数和闸函数,得到严格凸解的先验估计结果,进而利用连续性方法得到了该问题严格凸解的存在性。

关键词: Monge-Ampère方程；Neumann边界条件;先验估计

Abstract:

It is proved that a classical solution to the initial and Neumann boundary value problem for parabolic-type Monge-Ampère equation is existent and unique. Using compare principle, it is shown the uniqueness of the classical solution. By employing proper auxiliary functions and barrier functions, the priori estimations are obtained. The existence of the strict convex classical solution is obtained by the continuous method.

Key words: Monge-Ampère equation; Neumann boundary condition; priori estimation

王娟1,刘辉昭2. 一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题[J]. J4, 2010, 45(6): 70-73.

WANG Juan1, LIU Hui-zhao2. The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equations[J]. J4, 2010, 45(6): 70-73.

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