Approximate conservation laws of nonlinear perturbed heat and wave equations

被引：5

作者：

Bokhari, Ashfaque H. ^{[1
]}

Johnpillai, A. G.

Mahomed, F. M. ^{[2
,3
]}

Zaman, F. D. ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

[3] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, ZA-2050 Johannesburg, South Africa

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 06期

关键词：

Partial Lagrangian; Approximate partial Noether operators; Partial Noether theorem; Approximate conservation laws; SYMMETRIES; PDES; LAGRANGIANS;

D O I：

10.1016/j.nonrwa.2012.04.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct approximate conservation laws for non-variational nonlinear perturbed (1 + 1) heat and wave equations by utilizing the partial Lagrangian approach. These perturbed nonlinear heat and wave equations arise in a number of important applications which are reviewed. Approximate symmetries of these have been obtained in the literature. Approximate partial Noether operators associated with a partial Lagrangian of the underlying perturbed heat and wave equations are derived herein. These approximate partial Noether operators are then used via the approximate version of the partial Noether theorem in the construction of approximate conservation laws of the underlying perturbed heat and wave equations. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：2823 / 2829

页数：7

共 17 条

[1] On approximate Lagrangians and invariants for scaling reductions of a non-linear wave equation with damping
Ahmad, Ferhana
Kara, A. H.
Bokhari, A. H.
Zaman, F. D.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 206 (01) : 16 - 20
[2] A DAMPED HYPERBOLIC EQUATION WITH CRITICAL EXPONENT
ARRIETA, J
CARVALHO, AN
HALE, JK
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (5-6) : 841 - 866
[3] Baikov V., 1996, CRC HDB LIE GROUP AN, V3
[4] Carslaw H.S., 1986, Conduction of Heat In Solids, V2nde
[5] CATTANEO C, 1958, CR HEBD ACAD SCI, V247, P431
[6] SECOND SOUND IN SOLIDS
CHESTER, M
[J]. PHYSICAL REVIEW, 1963, 131 (05): : 2013 - &
[7] Approximate symmetries and solutions of the hyperbolic heat equation
Diatta, B.
Soh, C. Wafo
Khalique, C. M.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 205 (01) : 263 - 272
[8] Lie-Backlund and Noether symmetries with applications
Ibragimov, NH
Kara, AH
Mahomed, FM
[J]. NONLINEAR DYNAMICS, 1998, 15 (02) : 115 - 136
[9] Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter
Johnpillai, A. G.
Kara, A. H.
Mahomed, F. M.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (01) : 508 - 518
[10] A basis of approximate conservation laws for PDEs with a small parameter
Johnpillai, A. G.
Kara, A. H.
Mahomed, F. M.
[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (6-7) : 830 - 837

← 1 2 →