SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION 被引量：1

SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION

下载PDF

导出

摘要 In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed. In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed.

作者姚正安周文书

机构地区 Department of Mathematics

出处《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期581-601,共21页 数学物理学报（B辑英文版）

基金 Supported by National Natural Science Foundation of China(10171113 and 10471156) Natural Science Foundation of GuangDong 2004(4009793).

关键词 Degenerate and singular diffusion equation weak solution EXISTENCE asymptotic behavior Degenerate and singular diffusion equation, weak solution, existence, asymptotic behavior

分类号 O175.2 [理学—基础数学]

引文网络
相关文献

参考文献1

1周文书,伍卓群,高文杰.Some Results on a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form[J].Northeastern Mathematical Journal,2003,19(4):291-294. 被引量：5

二级参考文献13

1[13]Tsutsumi,M.,On solutions of some doubly nonlinear degenerate parabolic equations with absorption,J.Math.Anal.Appl.,132(1988),187-212.
2[1]Wu Zhuoqun,Zhao Junning,Yin Jingxue and Li Huilai,Nolinear Diffusion Equations,World Scientific Publishing Co.Pte.Ltd.,Singapore,2001.
3[2]Esteban,J.R.and Vazquez,J.L.,Homogeneous diffusion in R with power-like nonlinear diffusivity,Arch.Rat.Mech.Anal.,103(1)(1988),39-80.
4[3]Winkler,M.,Some results on degenerate parabolic equations not in divergence form,Ph.D.Thesis,RWTh Aachen,Germany,2000.
5[4]Dal Passo,R.and Luckhaus,S.,A degenerate diffusion problem not in divergence form,J.Differential Equations,69(1)(1987),1-14.
6[5]Bertsch,M.,Dal Passo,R.and Ughi,M.,Discontinuous viscosity solutions of a degenerate parabolic equation,Trans.Amer.Math.Soc.,320(2)(1990),779-798.
7[6]Bertsch,M.,Dal Passo,R.and Ughi,M.,Nonuniqueness of solutions of a degenerate parabolic equation,Ann.Mat.Pura Appl.,161(1992),57-81.
8[7]Bertsch,M.and Ughi,M.,Positivity property of viscosity solutions of a degenerate parabolic equation,Nonlinear Anal.,TMA,14(7)(1990),571-592.
9[8]Fukuda,I.,Ishii,H.and Tsutsumi,M.,Uniqueness of solutions to the Cauchy problem for ut - u△u +γ|∨u|2 = 0,Differential Integral Equations,6(6)(1993),1231-1252.
10[9]Zhan Yi,Theory of viscosity solutions and several classes of nonlinear degenerate equations,Ph.D.Thesis of Tsinghua University,Beijing,1993.

共引文献4

1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. 被引量：2
2周文书,蔡守峰.一类非散度型非线性抛物方程组Cauchy问题解的性质[J].吉林大学学报（理学版）,2005,43(4):402-406.
3姚正安,周文书,刘强.On a Singular Diffusion Equation in Nondivergence Form[J].数学进展,2005,34(4):503-505. 被引量：2
4CAO CHUN-LING CHENG XIAO-LIN GAO WEN-JIE.A Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form[J].Communications in Mathematical Research,2009,25(4):361-378.

同被引文献1

1曹春玲,林秉雄,汪宏梅.Existence of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form[J].Northeastern Mathematical Journal,2008,24(2):118-128. 被引量：1

引证文献1

1Yu-dong SUN,Yi-min SHI,MIN WU.Nonexistence and Longtime Behaviors of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form[J].Acta Mathematicae Applicatae Sinica,2016,32(2):327-332.

1潘佳庆.奇异扩散方程的非线性边值问题[J].数学进展,2000,29(1):71-76.
2潘佳庆.非线性奇异扩散方程解的存在性与唯一性[J].数学学报（中文版）,1999,42(3):537-544. 被引量：3
3潘佳庆.具非线性边界条件的奇异扩散方程[J].系统科学与数学,2002,22(2):144-148.
4王春朋,尹景学,伍卓群.Young Measure Solutions of a Class of Singular Diffusion Equations[J].Northeastern Mathematical Journal,2001,17(1):9-12.
5潘佳庆,雷英果.非线性奇异扩散方程的第二初边值问题[J].Journal of Mathematical Research and Exposition,1997,17(4):557-561. 被引量：3
6陈清婉,潘佳庆,柳文清.具源项的奇异扩散方程解的存在性及渐近性[J].数学研究,2010,43(3):264-272. 被引量：1
7詹华税,汤林冰.一类双重退化的奇异扩散方程[J].厦门理工学院学报,2014,22(5):88-92.
8YIN Jingxue and WANG Chunpeng(Department of Mathematics, Jilin University, Changchun 130012, China).Existence of Young measure solutions of a class of singular diffusion equations[J].Progress in Natural Science:Materials International,2002,12(4):258-263. 被引量：1
9叶金山,潘佳庆.一类奇异扩散方程解的若干估计[J].集美大学学报（自然科学版）,2013,18(6):467-470.
10姚正安,周文书,刘强.On a Singular Diffusion Equation in Nondivergence Form[J].数学进展,2005,34(4):503-505. 被引量：2

Acta Mathematica Scientia

2007年第3期

浏览历史

内容加载中请稍等...