The Cauchy problem for ut=Δu+|delu|q, large-time behaviour

被引：36

作者：

Gilding, BH ^{[1
]}

机构：

[1] Sultan Qaboos Univ, Coll Sci, Dept Math & Stat, Al Khoud, Oman

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2005年 / 84卷 / 06期

关键词：

surface growth; KPZ equation; viscous Hamilton-Jacobi equation; nonlinear second-order parabolic; temporal decay estimate; large-time behaviour;

D O I：

10.1016/j.matpur.2004.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nonlinear partial differential equation in the title is typified mathematically as a viscous Hamilton-Jacobi equation. It arises in the study of the growth of surfaces, and in that context is known as the generalized deterministic KPZ equation. Considering the Cauchy problem with initial data that are merely supposed to be bounded and continuous, results on the temporal decay and large-time behaviour of solutions are presented. Corresponding results for the heat equation serve as benchmarks. (c) 2004 Elsevier SAS. All rights reserved.

引用

页码：753 / 785

页数：33

共 50 条

[1] The Cauchy problem for ut = UDELTAu+|delu|q
Gilding, BH
Guedda, M
Kersner, R
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 284 (02) : 733 - 755
[2] Blowup for ut=Δu+|delu|2u from Rn into Rm
Hirata, D
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (06) : 1823 - 1827
[3] Existence of solutions of the Dirichlet problem for Δu+λu+h(u,delu)•delu=f(x)
Caliskan, N
Erkip, AK
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 39 (02) : 241 - 245
[4] Decay of mass for the equation ut = Δu-a(x) up |delu|q
Pinsky, RG
JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 165 (01) : 1 - 23
[5] Large-time behavior of solutions to the Cauchy problem for degenerate parabolic system
Tedeev, Anatoli F.
APPLICABLE ANALYSIS, 2022, 101 (02) : 460 - 470
[6] On the Cauchy problem for ut=Δlog u in higher dimensions
Daskalopoulos, P
del Pino, M
MATHEMATISCHE ANNALEN, 1999, 313 (02) : 189 - 206
[7] Large-Time Behaviour of Solutions of the Exterior-Domain Cauchy–Dirichlet Problem for the Porous Media Equation with Homogeneous Boundary Data
B. H. Gilding
J. Goncerzewicz
Monatshefte für Mathematik, 2007, 150 : 11 - 39
[8] Large-time behaviour of energy in elasticity
Qin, YM
Rivera, JEM
JOURNAL OF ELASTICITY, 2002, 66 (02) : 171 - 184
[9] Large-Time Behaviour of Energy in Elasticity
Yuming Qin
Jaime E. Muñoz Rivera
Journal of elasticity and the physical science of solids, 2002, 66 : 171 - 184
[10] BEHAVIOUR OF SOLUTION TO CAUCHY-POISSONS PROBLEM WITH A LARGE TIME
ISAKOVA, EK
DOKLADY AKADEMII NAUK SSSR, 1967, 176 (01): : 50 - &

← 1 2 3 4 5 →