退化抛物型方程弱解的存在性

周文华

数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 495-502.

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PDF(386 KB)
数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 495-502. DOI: 10.12386/A2010sxxb0055
论文

退化抛物型方程弱解的存在性

    周文华
作者信息 +

On the Existence of Weak Solutions to a Parabolic Equation of Degenerate Type for Semiconductors

    Wen Hua ZHOU
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摘要

讨论初值为u0, v0L+4(Ω), wW1,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u0, v0L+(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.

 

Abstract

The existence of the solution is discussed with u0, v0L+4(Ω), wW1,p(Ω) (p ≥ 2). Firstly a regularization of the problem with u0, v0L+(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.

 

关键词

退化抛物型方程 / 弱解 / 收敛性 / Gronwall引理 / 存在性

Key words

parabolic equations of degenerate type / the weak solution / the convergence / Gronwall’s lemma / existence

引用本文

导出引用
周文华. 退化抛物型方程弱解的存在性. 数学学报, 2010, 53(3): 495-502 https://doi.org/10.12386/A2010sxxb0055
Wen Hua ZHOU. On the Existence of Weak Solutions to a Parabolic Equation of Degenerate Type for Semiconductors. Acta Mathematica Sinica, Chinese Series, 2010, 53(3): 495-502 https://doi.org/10.12386/A2010sxxb0055

参考文献


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基金

淮海工学院科研课题资助项目(Z2007024)

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