| 一类非散度型退化抛物方程Cauchy问题粘性解的某种连续性 |
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| 引用本文： | 周文书,蔡守峰.一类非散度型退化抛物方程Cauchy问题粘性解的某种连续性[J].吉林大学学报(理学版),2004,42(3):341-345. |
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| 作者姓名： | 周文书 蔡守峰 |
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| 作者单位： | 吉林大学数学学院应用数学系,长春,130012;吉林大学数学学院应用数学系,长春,130012 |
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| 摘 要： | 研究一类非散度型退化抛物方程Cauchy问题粘性解的性质. 其中的粘性解是指用粘性消失法得到的分布意义下的弱解, 是惟一的. 利用研究弱解的技巧, 通过建立粘性解的一系列估计, 证明了粘性解关于某个参数(含在方程中)的连续性.
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| 关 键 词： | 粘性解 非散度型 退化抛物方程 连续性 |
| 文章编号： | 1671-5489(2004)03-0341-05 |
| 收稿时间： | 2004-01-06 |
| 修稿时间： | 2004年1月6日 |
Certain continuity of viscosity solutions of the Cauchy problem for a degenerate parabolic equations not in divergence form |
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| ZHOU Wen-shu,CAI Shou-feng.Certain continuity of viscosity solutions of the Cauchy problem for a degenerate parabolic equations not in divergence form[J].Journal of Jilin University: Sci Ed,2004,42(3):341-345. |
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| Authors: | ZHOU Wen-shu CAI Shou-feng |
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| Institution: | Department of Applied Mathematics, College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | The property of the viscosity solutions of the Cauchy problem of a degenerate parabolic equation not in divergence form is studied. The viscosity solution means a weak solution in the distribution sense obtained by the vanishing viscosity method. Using some techiques of studying weak solutions and establishing some estimates on the viscosity solution, we prove the continuity of the viscosity solution with respect to a parameter contained in the equations. |
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| Keywords: | viscosity solution not in divergence form degenerate parabolic equation continuity |
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