[1] Shi Peihu,. Self-similar very singular solution of a p-Laplacian equationwith gradient absorption: existence and uniqueness [J]. Journal of Southeast University (English Edition), 2004, 20 (3): 381-386. [doi:10.3969/j.issn.1003-7985.2004.03.024]

Copy

Self-similar very singular solution of a p-Laplacian equationwith gradient absorption: existence and uniqueness()

p-拉普拉斯方程的自相似奇性解: 存在惟一性

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

20

Issue:

2004 3

Page:

381-386

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2004-09-30

Info

Title:

Self-similar very singular solution of a p-Laplacian equationwith gradient absorption: existence and uniqueness

p-拉普拉斯方程的自相似奇性解: 存在惟一性

Author(s):

Shi Peihu

Department of Mathematics, Southeast University, Nanjing 210096, China

石佩虎

东南大学数学系, 南京 210096

Keywords:

p-Laplacian evolution equation;  gradient absorption;  self-similar;  singular solution;  very singular solution

p-拉普拉斯发展方程;  梯度吸收;  自相似;  奇性解;  强奇性解

PACS:

O157.5

DOI:

10.3969/j.issn.1003-7985.2004.03.024

Abstract:

This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u_t=div(|∇u|^p-2∇u)-|∇u|^q for 1<p<2 and q>1 in Rⁿ×(0, ∞). It has been proved that when 1<q<p-n/(n+1) there exists a unique self-similar very singular solution.

研究了p-拉普拉斯发展方程u_t=div(|∇u|^p-2∇u)-|∇u|^q 的自相似奇性解, 其中1<p<2, q>1, (x, t)∈Rⁿ×(0, ∞). 证明了当1<q<p-n/(n+1)时方程存在惟一的自相似强奇性解.

References:

[1] Shi Peihu. Self-similar singular solution of a p-Lapacian equation with gradient absorption terms [J]. J Partial Differential Equations, accepted to appear.
[2] Brezis H, Friedman A. Nonlinear parabolic equation involving measures as initial conditions [J]. J Math Pures Appl, 1983, 62(1): 73-97.
[3] Behachour S, Laurençot P. Very singular solutions to a nonlinear parabolic equation with absorption Ι existence [J]. Proceedings of the Royal Society Edinburgh, 2001, 131(1): 27-44.
[4] 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.
[5] Chen X, Qi Y, Wang M. Self-similar singular solution of a p-Laplacian evolution [J]. J Differential Equations, 2003, 190(1): 1-15.
[6] Peletier L A, Wang J. A very singular solution of a quasilinear degenerate diffusion equation with absorption [J]. Trans Amer Math Soc, 1988, 307(2): 813-826.
[7] Qi Y, Wang M. The self-similar profiles of generalized KPZ equation [J]. Pacific J of Math, 2001, 201(1): 223-240.

Memo

Memo:

Biography: Shi Peihu(1967—), male, lecturer, sph2106@yahoo.com.cn.

Common functions