| 一类带非局部项的Allen-Cahn方程解的存在性 |
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| 引用本文： | 刘桂兰.一类带非局部项的Allen-Cahn方程解的存在性[J].四川师范大学学报(自然科学版),2010,33(2). |
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| 作者姓名： | 刘桂兰 |
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| 作者单位： | 盐城工学院,基础教学部,江苏,盐城,224003 |
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| 基金项目： | 国家自然科学基金，江苏省高校自然科学基金 |
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| 摘 要： | 从图像处理中的修复、去噪与分割等问题出发,结合两相流的数学理论,提出了一类具有非局部项的Allen-Cahn方程的初边值问题,该方程与经典的Allen-Cahn方程相比,最大的不同之处是主部含有非局部项,然后利用Schauder不动点定理得到了带非局部项的Allen-Cahn方程初边值问题解的存在性.
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| 关 键 词： | Allen-Cahn方程 非局部项 初边值问题 |
The Existence of Solutions for a Class of Allen-Cahn Equations with Nonlocal Term |
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| LIU Gui-lan.The Existence of Solutions for a Class of Allen-Cahn Equations with Nonlocal Term[J].Journal of Sichuan Normal University(Natural Science),2010,33(2). |
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| Authors: | LIU Gui-lan |
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| Institution: | LIU Gui-lan(Department of Basic Courses,Yancheng Institute of Technology,Yancheng 224003,Jiangsu) |
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| Abstract: | In this paper,inspiring from the study on the reconstruction,denoising and segmentation in image processing,and combining with the theory of two phase fluids,the initial-boundary value problem for a class of Allen-Cahn equations with nonlocal term is introduced.Compared with the classical Allen-Cahn equation,this equation has the biggest difference in the principal part including the non-partial item.By using the Schauder fixed point theorem,the existence of weak solutions to the initial boundary value prob... |
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| Keywords: | Allen-Cahn equation nonlocal term initial-boundary value problem |
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