| 退化抛物型方程弱解的存在性 |
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| 引用本文： | 周文华.退化抛物型方程弱解的存在性[J].数学学报,2010,53(3):495-502. |
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| 作者姓名： | 周文华 |
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| 作者单位： | 淮海工学院理学院; |
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| 基金项目： | 淮海工学院科研课题资助项目(Z2007024) |
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| 摘 要： | 讨论初值为u_0,v_0∈L_+~4(Ω),w∈W~(1,p)(Ω)(p≥2)时退化抛物型方程弱解的存在性.首先利用截断的方法将原问题正则化,化为u_0,v_0∈L_+~∞(Ω)的退化问题,接着对正则化问题的解做估计(这里的估计与具体的截断无关),最后利用弱收敛性,通过取极限的方法证明了原问题解的存在性.
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| 关 键 词： | 退化抛物型方程 弱解 收敛性 Gronwall引理 存在性 |
| 收稿时间： | 2008-11-25 |
| 修稿时间： | 2009-10-27 |
On the Existence of Weak Solutions to a Parabolic Equation of Degenerate Type for Semiconductors |
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| Wen Hua ZHOU.On the Existence of Weak Solutions to a Parabolic Equation of Degenerate Type for Semiconductors[J].Acta Mathematica Sinica,2010,53(3):495-502. |
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| Authors: | Wen Hua ZHOU |
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| Institution: | Department of Mathematics and Physics Science Subjects, Huaihai Institute of Technology, Lianyungang 222005, P. R. China |
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| Abstract: | The existence of the solution is discussed with u0, v0 ∈ L+4(Ω), w ∈ W1,p(Ω) (p ≥ 2). Firstly a regularization of the problem with u0, v0 ∈ L+∞(Ω) is made by a cut-off method. By compact lemma it is proved that the limit of the solutions of the regularized problem is a solution of the original problem after estimates.
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| Keywords: | parabolic equations of degenerate type the weak solution the convergence Gronwall\'s lemma existence |
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