메뉴 건너뛰기




Volumn 49, Issue 1-2, 2007, Pages 71-81

Conservation laws of multidimensional diffusion - Convection equations

Author keywords

Conservation law; Diffusion equation; Equivalence transformations; Noether theorem; Symmetry

Indexed keywords

DIFFERENTIAL EQUATIONS; DIRECT NUMERICAL SIMULATION; LINEARIZATION; MATHEMATICAL TRANSFORMATIONS;

EID: 34248386474     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9104-2     Document Type: Article
Times cited : (8)

References (24)
  • 1
    • 0031490616 scopus 로고    scopus 로고
    • Nonlocal symmetries and nonlocal conservation laws of Maxwells equations
    • Anco, S.C., Bluman, G.: Nonlocal symmetries and nonlocal conservation laws of Maxwells equations. J. Math. Phys. 38, 3508-3532 (1997)
    • (1997) J. Math. Phys , vol.38 , pp. 3508-3532
    • Anco, S.C.1    Bluman, G.2
  • 2
    • 0036815244 scopus 로고    scopus 로고
    • Anco, S.C., Bluman, G.: Direct construction method for conservation laws of partial differential equations. I. Examples of conservation law classifications. Eur. J. Appl. Math. 13 (Part 5), 545-566 (2002) (math-ph/0108023)
    • Anco, S.C., Bluman, G.: Direct construction method for conservation laws of partial differential equations. I. Examples of conservation law classifications. Eur. J. Appl. Math. 13 (Part 5), 545-566 (2002) (math-ph/0108023)
  • 3
    • 0036813974 scopus 로고    scopus 로고
    • Anco, S.C., Bluman, G.: Direct construction method for conservation laws of partial differential equations. II. General treatment. Eur. J. Appl. Math. 13(Part 5), 567-585 (2002) (math-ph/0108024)
    • Anco, S.C., Bluman, G.: Direct construction method for conservation laws of partial differential equations. II. General treatment. Eur. J. Appl. Math. 13(Part 5), 567-585 (2002) (math-ph/0108024)
  • 4
    • 0016477678 scopus 로고
    • On the existence and formulation of variational principles for nonlinear differential equations
    • Atherton, R.W., Homsy, G.M.: On the existence and formulation of variational principles for nonlinear differential equations. Stud. Appl. Math. 54, 31-60 (1975)
    • (1975) Stud. Appl. Math , vol.54 , pp. 31-60
    • Atherton, R.W.1    Homsy, G.M.2
  • 6
    • 84990574706 scopus 로고
    • On singular diffusion equations with applications to self-organized criticality
    • Chayes, J.T., Osher, S.J., Ralston J.V.: On singular diffusion equations with applications to self-organized criticality. Commun. Pure Appl. Math. 46, 1363-1377 (1993)
    • (1993) Commun. Pure Appl. Math , vol.46 , pp. 1363-1377
    • Chayes, J.T.1    Osher, S.J.2    Ralston, J.V.3
  • 7
    • 34248384197 scopus 로고    scopus 로고
    • Chemina, R., King J.R.: Lie symmetries and conservation laws of non-linear multidimensional reactionñdiffusion systems with variable diffusivities. IMA J. Appl. Math. Adv. Access, September 23, 2005
    • Chemina, R., King J.R.: Lie symmetries and conservation laws of non-linear multidimensional reactionñdiffusion systems with variable diffusivities. IMA J. Appl. Math. Adv. Access, September 23, 2005
  • 8
    • 1842695585 scopus 로고
    • Wetting: Statics and dynamics
    • De Gennes, P.G.: Wetting: statics and dynamics. Rev. Modern Phys. 57, 827-863 (1985)
    • (1985) Rev. Modern Phys , vol.57 , pp. 827-863
    • De Gennes, P.G.1
  • 12
    • 0003689750 scopus 로고
    • Transformation groups applied to mathematical physics
    • Mathematics and Its Applications , D. Reidel Publishing Co, Dordrecht
    • Ibragimov, N.H.: Transformation groups applied to mathematical physics. Mathematics and Its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht (1985)
    • (1985) Soviet Series
    • Ibragimov, N.H.1
  • 13
    • 34248326247 scopus 로고    scopus 로고
    • Ibragimov, N.H.: (ed.) Lie group analysis of differential equations - symmetries, exact solutions and conservation laws, 1. Chemical Rubber Company, Boca Raton, FL (1994)
    • Ibragimov, N.H.: (ed.) Lie group analysis of differential equations - symmetries, exact solutions and conservation laws, Vol. 1. Chemical Rubber Company, Boca Raton, FL (1994)
  • 14
    • 3242777900 scopus 로고    scopus 로고
    • Lagrangian approach to evolution equations: Symmetries and conservation laws
    • Ibragimov, N.H., Kolsrud, T.: Lagrangian approach to evolution equations: symmetries and conservation laws. Nonlinear Dyn. 36, 29-40 (2004)
    • (2004) Nonlinear Dyn , vol.36 , pp. 29-40
    • Ibragimov, N.H.1    Kolsrud, T.2
  • 15
    • 34248338964 scopus 로고    scopus 로고
    • Ivanova, N.: Conservation laws and potential systems of diffusion-convection equations. In: Proceedings of Fifth International Conference on Symmetry in Nonlinear Mathematical Physics, Part 1, pp. 149-153, 23-29 June 2003, Kyiv Institute of Mathematics, Kyiv (2004) (math-ph/0404025)
    • Ivanova, N.: Conservation laws and potential systems of diffusion-convection equations. In: Proceedings of Fifth International Conference on "Symmetry in Nonlinear Mathematical Physics", Part 1, pp. 149-153, 23-29 June 2003, Kyiv Institute of Mathematics, Kyiv (2004) (math-ph/0404025)
  • 17
    • 84857213168 scopus 로고    scopus 로고
    • A basis of conservation laws for partial differential equations
    • Kara, A.H., Mahomed, F.M.: A basis of conservation laws for partial differential equations. J. Nonlinear Math. Phys. 9, 60-72 (2002)
    • (2002) J. Nonlinear Math. Phys , vol.9 , pp. 60-72
    • Kara, A.H.1    Mahomed, F.M.2
  • 18
    • 17444392262 scopus 로고
    • The structure of a group and the basis of conservation laws
    • Khamitova, R.S.: The structure of a group and the basis of conservation laws. Teoret. Mat. Fiz. 52(N 2), 244-251 (1982)
    • (1982) Teoret. Mat. Fiz , vol.52 , Issue.2 , pp. 244-251
    • Khamitova, R.S.1
  • 20
    • 17444394498 scopus 로고    scopus 로고
    • Popovych, R.O., Ivanova, N.M.: Hierarchy of conservation laws of diffusion-convection equations. J. Math. Phys. 46, 043502 (2005) (math-ph/0407008)
    • Popovych, R.O., Ivanova, N.M.: Hierarchy of conservation laws of diffusion-convection equations. J. Math. Phys. 46, 043502 (2005) (math-ph/0407008)
  • 21
    • 34247647193 scopus 로고    scopus 로고
    • Richard's, L.A.: Capillary conduction of liquids through porous mediums. Physics 1, 318-333 (1931)
    • Richard's, L.A.: Capillary conduction of liquids through porous mediums. Physics 1, 318-333 (1931)
  • 22
    • 34248395767 scopus 로고
    • On symmetries of the heat equation
    • Romanovsky, Y.R.: On symmetries of the heat equation. Acta Appl. Math. 15, 149-160 (1989)
    • (1989) Acta Appl. Math , vol.15 , pp. 149-160
    • Romanovsky, Y.R.1
  • 23
    • 34248397431 scopus 로고    scopus 로고
    • Vainberg, M.M.: Variational methods for investigation of non-linear operators (translation by Holden-Day, San Francisco, CA (1964). Gosudarstv. Izdat. Tehn-Teor. Lit. Moscow (1956) (in Russian)
    • Vainberg, M.M.: Variational methods for investigation of non-linear operators (translation by Holden-Day, San Francisco, CA (1964). Gosudarstv. Izdat. Tehn-Teor. Lit. Moscow (1956) (in Russian)
  • 24
    • 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 (Part 5), 129-152 (2002)
    • (2002) Eur. J. Appl. Math , vol.13 , Issue.PART 5 , pp. 129-152
    • Wolf, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.