[1]黄小萍,曾有栋.一类带退化扩散的哈密尔顿-雅克比方程组的适定性[J].华侨大学学报(自然科学版),2013,34(3):339-343.[doi:10.11830/ISSN.1000-5013.2013.03.0339]
　HUANG Xiao-ping,ZENG You-dong.Well-Posedness for a Hamilton-Jacobi System with Degenerate Diffusion[J].Journal of Huaqiao University(Natural Science),2013,34(3):339-343.[doi:10.11830/ISSN.1000-5013.2013.03.0339]
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一类带退化扩散的哈密尔顿-雅克比方程组的适定性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第3期
页码:
339-343
栏目:
出版日期:
2013-05-20

文章信息/Info

Title:
Well-Posedness for a Hamilton-Jacobi System with Degenerate Diffusion
文章编号:
1000-5013(2013)03-0339-05
作者:
黄小萍;  曾有栋
福州大学 数学与计算机科学学院, 福建 福州 350108
Author(s):
HUANG Xiao-ping;  ZENG You-dong
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China
关键词:
哈密尔顿-雅克比方程组;  适定性;  弱解;  局部存在性;  爆破二择一;  正则性
Keywords:
Hamilton-Jacobi system;  well-posedness;  weak solutions;  local existence;  blow up alternative;  regularizing effect
分类号:
O175.02
DOI:
10.11830/ISSN.1000-5013.2013.03.0339
文献标志码:
A
摘要:
讨论带狄利克雷边界条件的退化扩散哈密尔顿-雅克比方程组?tu-div(|?u|p1-2?u)=|?v|q1,?tv-div(|?v|p2-2?v)=|?u|q2的弱解性质,其中Ω
Abstract:
This paper discusses the properties of weak solutions to a degenerate viscous Hamilton-Jacobi system ?tu-div(|?u|p1-2?u)=|?v|q1,?tv-div(|?v|p2-2?v)=|?u|q2, with Dirichlet boundary conditions in a bounded domain Ω?RN, where qi>max{(p1-1),(p2-1)} and pi>2,i=1,2. We constructe a unique, maximal in time, W1,∞×W1,∞ solution, without size restriction on the initial data and to establish the blow up alternative in W1,∞×W1,∞ norm. Furthermore, we also obtain a regularizing effect for(ut,vt).

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2012-11-12
通信作者: 曾有栋(1961-),男,教授,主要从事偏微分方程的研究.E-mail:zengyd@fzu.edu.cn.
基金项目: 福建省自然科学基金资助项目(Z0511015)
更新日期/Last Update: 2013-05-20