带梯度吸收项的快扩散方程的自相似奇性解

石佩虎; 王明新

带梯度吸收项的快扩散方程的自相似奇性解

东南大学数学系,南京 210096

基金项目: 国家自然科学基金资助项目(10471022);教育部科学技术基金(重点)资助项目(104090)

详细信息

作者简介:
石佩虎(1967- ),男,湖南省花垣县人,副教授,博士(联系人.E-mail:sph2106@yahoo.com.cn).

中图分类号: O175.26
计量
- 文章访问数: 3038
- HTML全文浏览量: 257
- PDF下载量: 667
- 被引次数: 0
出版历程
- 收稿日期: 2004-05-28
- 修回日期: 2006-10-09
- 刊出日期: 2007-01-15

Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms

Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

摘要

摘要: 研究一类带有非线性梯度吸收项的快速扩散方程的自相似奇性解．通过自相似变换,该自相似奇性解满足一个非线性常微分方程的边值问题，再利用打靶法技巧研究该常微分方程初值问题解的存在唯一性并根据初值的取值范围对其解进行了分类．通过对这些解类的性质的分析研究，得出了自相似强奇性解存在唯一性的充分必要条件，此时自相似奇性解就是强奇性解．
- 快扩散方程 /
- 梯度吸收 /
- 自相似奇性解 /
- 强奇性解
Abstract: The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms had been studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ODE. Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE had been investigated, the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by the investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.
- fast diffusion equation /
- gradient absorption /
- self-similar singular solution /
- very singular solution

HTML全文

参考文献(14)

[1]	Kardar M,Parisi G,Zhang Y C.Dynamic scaling of growing interface[J].Phys Rev Lett,1986,56(9):889-892. doi: 10.1103/PhysRevLett.56.889
[2]	Krug J,Spohn H.Universisality classes for deterministic surface growth[J].Phys Rev A,1988,38(8):4271-4283. doi: 10.1103/PhysRevA.38.4271
[3]	Bebachour S,Laurenot Ph.Very singular solutions to a nonliear parabolic equation with absorption. I. Existence[J].Proc the Royal Soc Edinberg,2001,131(A)(1):27-44. doi: 10.1017/S0308210500000779
[4]	QI Yuan-wei,WANG Ming-xin.The self-similar profiles of generalized KPZ equation[J].Pacific J of Math,2001,201(1):223-240. doi: 10.2140/pjm.2001.201.223
[5]	Brezis H,Friedman A.Nonlinear parabolic equation involving measures as initial conditions[J].J Math Pures Appl,1983,62(1):73-97.
[6]	Brezis H,Peletier L A,Terman D.A very singular solution of the heat equation with absorption[J].Arch Rational Mech Anal,1986,95(3):185-209.
[7]	CHEN Xin-fu,QI Yuan-wei,WANG Ming-xin.Self-similar singular solution of a p-Laplacian evolution[J].J Differential Equations,2003,190(1):1-15. doi: 10.1016/S0022-0396(02)00039-6
[8]	Kamin S,Vazquez J L.Singular solutions of some nonlinear parabolic equation[J].J Anal Math,1992,59(1):51-74. doi: 10.1007/BF02790217
[9]	Leoni G.A very singular solution for the porous media equation ut=Δ(um)-up when 0＜m＜1[J].J Diff Eqns,1996,132(2):353-376. doi: 10.1006/jdeq.1996.0184
[10]	Peletier L A,WANG Jun-yu.A very singular solution of a quasilinear degenerate diffusion equation with absorption[J].Trans Amer Math Soc,1988,307(2):813-826. doi: 10.1090/S0002-9947-1988-0940229-6
[11]	CHEN Xin-fu,QI Yuan-wei,WANG Ming-xin.Long time behavior of solutions to p-Laplacian equation with absorption[J].SIAM J Appl Math,2003,35(1):123-134. doi: 10.1137/S0036141002407727
[12]	Escobedo M,Kavian O,Matano H.Large time behavior of solutions of a dissipative semilinesr heat equation[J].Commun Partial Diff Eqns,1995,20(8):1427-1452. doi: 10.1080/03605309508821138
[13]	Herraiz L.Asymptotic behaviour of solutions of some semilinear parabolic problems[J].Ann Inst Henri　Poicaré,1999,16(1):49-104.
[14]	Kwak M.A porous media equation with absorption I. Long time behaviour[J].J Math Anal & Appl,1998,223(1):96-110.