메뉴 건너뛰기




Volumn 205, Issue 1, 2008, Pages 212-230

Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics

Author keywords

Characteristic method; Conservation laws; Direct construction formula approach; Direct method; Noether approach for the system and its adjoint; Noether's theorem; Partial Noether approach; Symmetry conditions; Variational approach for arbitrary functions and on the solution space

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL FLUID DYNAMICS; CONTACTS (FLUID MECHANICS); DISTRIBUTION FUNCTIONS; FLUID MECHANICS; IMAGE SEGMENTATION; LINEAR EQUATIONS; MECHANICS; PROBABILITY DENSITY FUNCTION;

EID: 54049148104     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.06.042     Document Type: Review
Times cited : (189)

References (17)
  • 1
    • 54049130974 scopus 로고    scopus 로고
    • R. Naz, D.P. Mason, F.M. Mahomed, Conservation laws and physical conserved quantities for laminar two-dimensional and radial jets, J. Nonlinear Anal. B: Real World Appl., submitted for publication.
    • R. Naz, D.P. Mason, F.M. Mahomed, Conservation laws and physical conserved quantities for laminar two-dimensional and radial jets, J. Nonlinear Anal. B: Real World Appl., submitted for publication.
  • 2
    • 0001504634 scopus 로고
    • Invariante Variationsprobleme
    • (English translation in Transport Theory and Statistical Physiscs 1 (3) (1971) 186-207)
    • Noether E. Invariante Variationsprobleme. Nacr. Konig. Gesell. Wissen., Gottingen, Math.-Phys. Kl. Heft 2 (1918) 235-257 (English translation in Transport Theory and Statistical Physiscs 1 (3) (1971) 186-207)
    • (1918) Nacr. Konig. Gesell. Wissen., Gottingen, Math.-Phys. Kl. Heft , vol.2 , pp. 235-257
    • Noether, E.1
  • 3
    • 54049142612 scopus 로고    scopus 로고
    • P.S. Laplace (English translation, Celestrial Mechanics, New York, 1966), 1798.
    • P.S. Laplace (English translation, Celestrial Mechanics, New York, 1966), 1798.
  • 4
    • 84927137412 scopus 로고
    • Uber die zuordnung zwischen invarianzeigenschaften und erhaltungssatzen
    • Steudel H. Uber die zuordnung zwischen invarianzeigenschaften und erhaltungssatzen. Z. Naturforsch. 17A (1962) 129-132
    • (1962) Z. Naturforsch. , vol.17 A , pp. 129-132
    • Steudel, H.1
  • 6
    • 0036815244 scopus 로고    scopus 로고
    • Direct construction method for conservation laws of partial differential equations. Part I: Examples of conservation law classifications
    • Anco S.C., and Bluman G.W. Direct construction method for conservation laws of partial differential equations. Part I: Examples of conservation law classifications. Eur. J. Appl. Math. 13 (2002) 545-566
    • (2002) Eur. J. Appl. Math. , vol.13 , pp. 545-566
    • Anco, S.C.1    Bluman, G.W.2
  • 7
    • 0036813974 scopus 로고    scopus 로고
    • Direct construction method for conservation laws of partial differential equations. Part II: General treatment
    • Anco S.C., and Bluman G.W. Direct construction method for conservation laws of partial differential equations. Part II: General treatment. Eur. J. Appl. Math. 9 (2002) 567-585
    • (2002) Eur. J. Appl. Math. , vol.9 , pp. 567-585
    • Anco, S.C.1    Bluman, G.W.2
  • 8
    • 0036013711 scopus 로고    scopus 로고
    • A comparison of four approaches to the calculation of conservation laws
    • Wolf T. A comparison of four approaches to the calculation of conservation laws. Eur. J. Appl. Math. 13 (2002) 129-152
    • (2002) Eur. J. Appl. Math. , vol.13 , pp. 129-152
    • Wolf, T.1
  • 9
    • 0034378632 scopus 로고    scopus 로고
    • Relationship between symmetries and conservation laws
    • Kara A.H., and Mahomed F.M. Relationship between symmetries and conservation laws. Int. J. Theor. Phys. 39 (2000) 23-40
    • (2000) Int. J. Theor. Phys. , vol.39 , pp. 23-40
    • Kara, A.H.1    Mahomed, F.M.2
  • 10
    • 33746208819 scopus 로고    scopus 로고
    • Noether-type symmetries and conservation laws via partial Lagragians
    • Kara A.H., and Mahomed F.M. Noether-type symmetries and conservation laws via partial Lagragians. Nonlinear Dynam. 45 (2006) 367-383
    • (2006) Nonlinear Dynam. , vol.45 , pp. 367-383
    • Kara, A.H.1    Mahomed, F.M.2
  • 11
    • 0016477678 scopus 로고
    • On the existence and formulation of variational principles for nonlinear differential equations
    • Atherton R.W., and Homsy G.M. On the existence and formulation of variational principles for nonlinear differential equations. Studies Appl. Math. 54 (1975) 31-60
    • (1975) Studies Appl. Math. , vol.54 , pp. 31-60
    • Atherton, R.W.1    Homsy, G.M.2
  • 12
    • 34248188617 scopus 로고    scopus 로고
    • A new conservation theorem
    • Ibragimov N.H. A new conservation theorem. J. Math. Anal. Appl. 333 (2007) 311-328
    • (2007) J. Math. Anal. Appl. , vol.333 , pp. 311-328
    • Ibragimov, N.H.1
  • 13
    • 0039860402 scopus 로고
    • Symmetry vector fields and similarity solutions of nonlinear field equation describing the relaxation to a Maxwell distribution
    • Euler N., Leach P.G., Mahomed F.M., and Steeb W.-H. Symmetry vector fields and similarity solutions of nonlinear field equation describing the relaxation to a Maxwell distribution. Int. J. Theor. Phys. 27 (1988) 717-723
    • (1988) Int. J. Theor. Phys. , vol.27 , pp. 717-723
    • Euler, N.1    Leach, P.G.2    Mahomed, F.M.3    Steeb, W.-H.4
  • 14
    • 0035452981 scopus 로고    scopus 로고
    • Non-linear diffusion of an axisymmetric thin liquid drop: group invariant solution and conservation law
    • Momoniat E., Mason D.P., and Mahomed F.M. Non-linear diffusion of an axisymmetric thin liquid drop: group invariant solution and conservation law. Int. J. Nonlinear Mech. 36 (2001) 879-885
    • (2001) Int. J. Nonlinear Mech. , vol.36 , pp. 879-885
    • Momoniat, E.1    Mason, D.P.2    Mahomed, F.M.3
  • 16
    • 54049083585 scopus 로고    scopus 로고
    • R. Naz, D.P. Mason, F.M. Mahomed, Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets, J. Nonlinear Anal. B: Real World Appl., submitted for publication.
    • R. Naz, D.P. Mason, F.M. Mahomed, Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets, J. Nonlinear Anal. B: Real World Appl., submitted for publication.
  • 17
    • 0642277016 scopus 로고
    • The radial free jet
    • Schwarz W.H. The radial free jet. Chem. Eng. Sci. 18 (1963) 779-786
    • (1963) Chem. Eng. Sci. , vol.18 , pp. 779-786
    • Schwarz, W.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.