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一类带时滞的非线性抛物方程理论分析
  • ISSN号：1006-2467
  • 期刊名称：《上海交通大学学报》
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]丽水学院教育学院,浙江丽水323000
  • 相关基金：国家自然科学基金资助项目（10531020,10676020）,浙江省自然科学基金资助项目（Y6090681）,浙江省教育厅科研项目（Y201120509）,丽水学院重点科研项目（KZ20i130,KZ201131）
作者： 吴慧伶[1]
关键词： 非线性抛物方程, 时滞, 非局部项, 适定性, 图像处理, nonlinear parabolic equation, time-delay, a nonlocal term, well-posedness, image processing
中文摘要：

以图像处理中的去噪问题为背景，研究了一类带时滞和非局部项的非线性抛物方程初边值问题．利用能量估计、不动点定理理论等分析方法，建立了一类带时滞和非局部项的非线性抛物方程初边值问题弱解的存在性、惟一性和稳定性．对该问题的适定性特别是稳定性的讨论，将有利于进一步对图像进行数值模拟．

英文摘要：

Based on the denoising problem in image processing, the well-posedness of the initial-boundary value problem for a nonlinear parabolic equation with time delay and a nonlocal term was studied. By using energy estimates and the fixed point theorem,the existence, uniqueness and stability of the weak solution to this initial-boundary problem were investigated. This study is helpful for the numerical simulation in image processing.

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期刊信息
  • 《上海交通大学学报》
  • 中国科技核心期刊
  • 主管单位:中华人民共和国教育部
  • 主办单位:上海交通大学
  • 主编：郑杭
  • 地址：上海市华山路1954号15F
  • 邮编：200030
  • 邮箱：shjt@chinajournal.net.cn
  • 电话：021-62933373 62932534
  • 国际标准刊号：ISSN：1006-2467
  • 国内统一刊号：ISSN：31-1466/U
  • 邮发代号:4-256
  • 获奖情况:
  • 1996年全国优秀科技期刊奖,1992年、1996年、1999年国家教育部系统优秀科技期刊奖,2002年“百种重点期刊奖”,2003年百种中国杰出学术期刊,2004年教育部全国高校优秀科技期刊一等奖,2004年“百种重点期刊奖”
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  • 被引量:30903