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Volumn 38, Issue 5, 1997, Pages 978-987

New exact solutions of the one-dimensional nonlinear diffusion equation

(2)  Rudykh, G A a   Semenov E I a  

a NONE

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EID: 27544508509     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02673043     Document Type: Article
Times cited : (6)

References (36)
  • 1
    • 0001017624 scopus 로고
    • Note sur la theorie de la variation des constantes arbitraires
    • J. Liouville, "Note sur la theorie de la variation des constantes arbitraires," J. Math. Pures Appl., No. 3, 342-349 (1838).
    • (1838) J. Math. Pures Appl. , Issue.3 , pp. 342-349
    • Liouville, J.1
  • 2
    • 27544508405 scopus 로고
    • Sur les systemes physiques avec les conditions initiales aleatoires
    • S. Guiasu, "Sur les systemes physiques avec les conditions initiales aleatoires," Rev. Roumaine Math. Pures Appl., 12, No. 9, 1271-1281 (1967).
    • (1967) Rev. Roumaine Math. Pures Appl. , vol.12 , Issue.9 , pp. 1271-1281
    • Guiasu, S.1
  • 3
    • 0006654191 scopus 로고
    • Generalized Liouville equation, entropy and dynamic systems containing limit cycles
    • W. H. Steeb, "Generalized Liouville equation, entropy and dynamic systems containing limit cycles," Phys. A, 95, No. 1, 181-190 (1979).
    • (1979) Phys. A , vol.95 , Issue.1 , pp. 181-190
    • Steeb, W.H.1
  • 4
    • 27544463022 scopus 로고
    • A global existence theorem for a nonlinear system and the deficiency index of a linear operator
    • A. Ya. Povzner, "A global existence theorem for a nonlinear system and the deficiency index of a linear operator," Sibirsk. Mat. Zh., 5, No. 2, 377-386 (1964).
    • (1964) Sibirsk. Mat. Zh. , vol.5 , Issue.2 , pp. 377-386
    • Povzner, A.Ya.1
  • 9
    • 27544479435 scopus 로고
    • The generalized Liouville equation in studying stability of nonautonomous systems
    • Nauka, Novosibirsk
    • G. A. Rudykh, "The generalized Liouville equation in studying stability of nonautonomous systems," in: Dynamics of Nonlinear Systems [in Russian], Nauka, Novosibirsk, 1983, pp. 141-151.
    • (1983) Dynamics of Nonlinear Systems [in Russian] , pp. 141-151
    • Rudykh, G.A.1
  • 10
    • 27544509414 scopus 로고
    • A relation between the Liouville theorem for a nonautonomous system of differential equations and stability of motion
    • Nauka, Novosibirsk
    • G. A. Rudykh, "A relation between the Liouville theorem for a nonautonomous system of differential equations and stability of motion," in: The Method of Lyapunov Functions and Its Applications [in Russian], Nauka, Novosibirsk, 1984, pp. 151-170.
    • (1984) The Method of Lyapunov Functions and Its Applications [in Russian] , pp. 151-170
    • Rudykh, G.A.1
  • 11
    • 3542999152 scopus 로고
    • Vers une description non conservative de l'evolution en physique
    • J. Fronteau, "Vers une description non conservative de l'evolution en physique," Hadronic J., 2, No. 4, 727-829 (1979).
    • (1979) Hadronic J. , vol.2 , Issue.4 , pp. 727-829
    • Fronteau, J.1
  • 12
    • 27544455770 scopus 로고
    • Properties of an integral curve and solutions of a nonautonomous system of differential equations
    • Nauka, Novosibirsk
    • G. A. Rudykh, "Properties of an integral curve and solutions of a nonautonomous system of differential equations," in: Lyapunov Functions and Their Applications [in Russian], Nauka, Novosibirsk, 1987, pp. 189-198.
    • (1987) Lyapunov Functions and Their Applications [in Russian] , pp. 189-198
    • Rudykh, G.A.1
  • 13
    • 0000861379 scopus 로고
    • A Lie-admissible method of integration of Fokker-Planck equations with nonlinear coefficients (exact and numerical solutions)
    • J. Fronteau and P. Combis, "A Lie-admissible method of integration of Fokker-Planck equations with nonlinear coefficients (exact and numerical solutions)," Hadronic J., 7, 911-930 (1984).
    • (1984) Hadronic J. , vol.7 , pp. 911-930
    • Fronteau, J.1    Combis, P.2
  • 14
    • 27544473730 scopus 로고
    • Quasidifferential systems associated to some equations of evolution
    • A. Chaljub-Simon and J. Fronteau, "Quasidifferential systems associated to some equations of evolution," Hadronic J., 9, No. 6, 291-300 (1986).
    • (1986) Hadronic J. , vol.9 , Issue.6 , pp. 291-300
    • Chaljub-Simon, A.1    Fronteau, J.2
  • 16
    • 27544496520 scopus 로고
    • Application of Liouville's equation to construction of special exact solutions for the quasilinear heat equation
    • G. A. Rudykh and E. I. Semenov, "Application of Liouville's equation to construction of special exact solutions for the quasilinear heat equation," IMACS Ann. Comput. Appl. Math., 8, 193-196 (1990).
    • (1990) IMACS Ann. Comput. Appl. Math. , vol.8 , pp. 193-196
    • Rudykh, G.A.1    Semenov, E.I.2
  • 18
    • 0039749020 scopus 로고
    • A construction of exact solutions to a many-dimensional quasilinear heat equation
    • G. A. Rudykh and È. I. Semënov, "A construction of exact solutions to a many-dimensional quasilinear heat equation," Zh. Vychisl. Mat. i Mat. Fiz., 33, No. 8, 1228-1239 (1993).
    • (1993) Zh. Vychisl. Mat. i Mat. Fiz. , vol.33 , Issue.8 , pp. 1228-1239
    • Rudykh, G.A.1    Semënov, È.I.2
  • 23
    • 0013406837 scopus 로고
    • Study of polynomial solutions of the gas filtration equations with an integral exponent of the adiabatic curve
    • Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk
    • S. S. Titov and V. A. Ustinov, "Study of polynomial solutions of the gas filtration equations with an integral exponent of the adiabatic curve," in: Approximate Methods for Solving Boundary Value Problems of Continuum Mechanics [in Russian], Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk, 1985, pp. 64-79.
    • (1985) Approximate Methods for Solving Boundary Value Problems of Continuum Mechanics [in Russian] , pp. 64-79
    • Titov, S.S.1    Ustinov, V.A.2
  • 24
    • 0038203026 scopus 로고
    • Equivalence transformations and hidden symmetry of evolution equations
    • V. V. Pukhnachëv, "Equivalence transformations and hidden symmetry of evolution equations," Dokl. Akad. Nauk SSSR, 294, No. 3, 535-538 (1987).
    • (1987) Dokl. Akad. Nauk SSSR , vol.294 , Issue.3 , pp. 535-538
    • Pukhnachëv, V.V.1
  • 25
    • 0000121198 scopus 로고
    • On new exact solutions to parabolic equations with quadratic nonlinearities
    • V. A. Galaktionov and S. A. Posashkov, "On new exact solutions to parabolic equations with quadratic nonlinearities," Zh. Vychisl. Mat. i Mat. Fiz., 29, No. 4, 497-506 (1989).
    • (1989) Zh. Vychisl. Mat. I Mat. Fiz. , vol.29 , Issue.4 , pp. 497-506
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 26
    • 84972500466 scopus 로고
    • On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
    • V. A. Galaktionov, "On new exact blow-up solutions for nonlinear heat conduction equations with source and applications," Differential Integral Equations, 3, No. 5, 863-874 (1990).
    • (1990) Differential Integral Equations , vol.3 , Issue.5 , pp. 863-874
    • Galaktionov, V.A.1
  • 28
    • 0027646569 scopus 로고
    • Exact multidimensional solutions to some nonlinear diffusion equations
    • J. R. King, "Exact multidimensional solutions to some nonlinear diffusion equations," Quart. J. Mech. Appl. Math., 46, No. 3, 419-436 (1993).
    • (1993) Quart. J. Mech. Appl. Math. , vol.46 , Issue.3 , pp. 419-436
    • King, J.R.1
  • 29
    • 0011298627 scopus 로고
    • Exact solutions and invariant spaces for nonlinear equations of gradient diffusion
    • V. A. Galaktionov and S. A. Posashkov, "Exact solutions and invariant spaces for nonlinear equations of gradient diffusion," Zh. Vychisl. Mat. i Mat. Fiz., 34, No. 3, 373-383 (1994).
    • (1994) Zh. Vychisl. Mat. i Mat. Fiz. , vol.34 , Issue.3 , pp. 373-383
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 30
    • 0000654014 scopus 로고
    • Generalized separation of variables for differential equations with polynomial nonlinearities
    • V. A. Galaktionov, S. A. Posashkov, and S. R. Svirshchevskiǐ, "Generalized separation of variables for differential equations with polynomial nonlinearities," Differentsial'nye Uravneniya, 31, No. 2, 253-261 (1995).
    • (1995) Differentsial'nye Uravneniya , vol.31 , Issue.2 , pp. 253-261
    • Galaktionov, V.A.1    Posashkov, S.A.2    Svirshchevskiǐ, S.R.3
  • 31
    • 0039156642 scopus 로고
    • On anisotropic exact solutions of a multidimensional equation of nonstationary filtration
    • E. R. Kosygina, "On anisotropic exact solutions of a multidimensional equation of nonstationary filtration," Zh. Vychisl. Mat. i Mat. Fiz., 35, No. 2, 241-259 (1995).
    • (1995) Zh. Vychisl. Mat. i Mat. Fiz. , vol.35 , Issue.2 , pp. 241-259
    • Kosygina, E.R.1
  • 32
    • 0039749010 scopus 로고
    • Multidimensional exact solutions of a nonlinear diffusion equation
    • V. V. Pukhnachëv, "Multidimensional exact solutions of a nonlinear diffusion equation," Prikl. Mekh. Tekhn. Fiz., 36, No. 2, 23-31 (1995).
    • (1995) Prikl. Mekh. Tekhn. Fiz. , vol.36 , Issue.2 , pp. 23-31
    • Pukhnachëv, V.V.1
  • 33
    • 84971166861 scopus 로고
    • Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
    • V. A. Galaktionov, "Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities," Proc. Roy. Soc. Edinburgh Sect. A, 125 No. 2, 225-246 (1995).
    • (1995) Proc. Roy. Soc. Edinburgh Sect. A , vol.125 , Issue.2 , pp. 225-246
    • Galaktionov, V.A.1
  • 36
    • 0007133626 scopus 로고
    • Group theoretic properties of the heat equation with a source in two-dimensional and three-dimensional cases
    • V. A. Dorodnitsyn, I. V. Knyazeva, and S. R. Svirshchevskiǐ, "Group theoretic properties of the heat equation with a source in two-dimensional and three-dimensional cases," Differentsial'nye Uravneniya, 19, No. 7, 1215-1223 (1983).
    • (1983) Differentsial'nye Uravneniya , vol.19 , Issue.7 , pp. 1215-1223
    • Dorodnitsyn, V.A.1    Knyazeva, I.V.2    Svirshchevskiǐ, S.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.