| Existence of Young measure solutions of a class of singular diffusion equations |
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| 作者姓名： | YIN Jingxue WANG Chunpeng |
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| 作者单位： | Department of Mathematics, Jilin University, Changchun 130012, China,Department of Mathematics, Jilin University, Changchun 130012, China |
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| 基金项目： | Supported by the Ministry of Science and Technology of China |
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| 摘 要： | The first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity is investigated. Such equations may be strongly degenerate, singular and forward-backward. Inspired by the idea in a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence of such solutions. Consequently, we approximate the extreme case by the method of regularization. By means of some uniform estimates and some techniques, the existence of Young measure solutions with bounded variation is established.
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| 关 键 词： | singular diffusion equations forward-backward Young measure solutions |
Existence of Young measure solutions of a class of singular diffusion equations |
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| YIN Jingxue,WANG Chunpeng.Existence of Young measure solutions of a class of singular diffusion equations[J].Progress in Natural Science,2002,12(4):258-263. |
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| Authors: | YIN JINGXUE Wang Chunpeng |
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| Institution: | Department of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | The first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity is investigated. Such equations may be strongly degenerate, singular and forward-backward. Inspired by the idea in a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence of such solutions. Consequently, we approximate the extreme case by the method of regularization. By means of some uniform estimates and some techniques, the existence of Young measure solutions with bounded variation is established. |
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| Keywords: | singular diffusion equations forward-backward Young measure solutions |
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