메뉴 건너뛰기




Volumn 57, Issue 5, 1997, Pages 1189-1215

An organizing center for wave bifurcation in multiphase flow models

Author keywords

Melnikov's method; Riemann problems; Shock waves; Viscous profiles

Indexed keywords

BIFURCATION (MATHEMATICS); MATHEMATICAL MODELS; POROUS MATERIALS; PROBLEM SOLVING; SHOCK WAVES; VISCOUS FLOW;

EID: 0031258897     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139995280683     Document Type: Article
Times cited : (9)

References (19)
  • 1
    • 0000467530 scopus 로고
    • Multiple viscous solutions for systems of conservation laws
    • A. AZEVEDO AND D. MARCHESIN, Multiple viscous solutions for systems of conservation laws, Trans. Amer. Math. Soc., 347 (1995), pp. 3061-3078.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 3061-3078
    • Azevedo, A.1    Marchesin, D.2
  • 2
    • 0030521408 scopus 로고    scopus 로고
    • Nonuniqueness of nonclassical solutions of Riemann problems
    • A. AZEVEDO, D. MARCHESIN, B. PLOHR, AND K. ZUMBRUN, Nonuniqueness of nonclassical solutions of Riemann problems, Z. Angew. Math. Phys., 47 (1996), pp. 977-998.
    • (1996) Z. Angew. Math. Phys. , vol.47 , pp. 977-998
    • Azevedo, A.1    Marchesin, D.2    Plohr, B.3    Zumbrun, K.4
  • 4
    • 0004496464 scopus 로고
    • Stability of singular fundamental solutions under perturbations for flow in porous media
    • A. DE SOUZA, Stability of singular fundamental solutions under perturbations for flow in porous media, Mat. Apl. Comput., 11 (1992), pp. 73-115.
    • (1992) Mat. Apl. Comput. , vol.11 , pp. 73-115
    • De Souza, A.1
  • 6
    • 0345260622 scopus 로고
    • A global formalism for nonlinear waves in conservation laws
    • E. ISAACSON, D. MARCHESIN, C. F. PALMEIRA, AND B. PLOHR, A global formalism for nonlinear waves in conservation laws, Comm. Math. Phys., 146 (1992), pp. 505-552.
    • (1992) Comm. Math. Phys. , vol.146 , pp. 505-552
    • Isaacson, E.1    Marchesin, D.2    Palmeira, C.F.3    Plohr, B.4
  • 7
    • 0001383243 scopus 로고
    • The Riemann problem near a hyperbolic singularity: The classification of quadratic Riemann problems I
    • E. ISAACSON, D. MARCHESIN, B. PLOHR, AND J. B. TEMPLE, The Riemann problem near a hyperbolic singularity: the classification of quadratic Riemann problems I, SIAM J. Appl. Math., 48 (1988), pp. 1009-1032.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 1009-1032
    • Isaacson, E.1    Marchesin, D.2    Plohr, B.3    Temple, J.B.4
  • 9
    • 0001383244 scopus 로고
    • The Riemann problem near a hyperbolic singularity II
    • E. ISAACSON AND J. B. TEMPLE, The Riemann problem near a hyperbolic singularity II, SIAM J. Appl. Math., 48 (1988), pp. 1287-1301.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 1287-1301
    • Isaacson, E.1    Temple, J.B.2
  • 10
    • 0004525954 scopus 로고
    • The Riemann problem near a hyperbolic singularity III
    • E. ISAACSON AND J. B. TEMPLE, The Riemann problem near a hyperbolic singularity III, SIAM J. Appl. Math., 48 (1988), pp. 1302-1312.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 1302-1312
    • Isaacson, E.1    Temple, J.B.2
  • 11
    • 0001834849 scopus 로고
    • On the stability of the center for time periodic perturbations
    • V. K. MELNIKOV, On the stability of the center for time periodic perturbations, Trans. Moscow Math. Soc., 12 (1963), pp. 1-57.
    • (1963) Trans. Moscow Math. Soc. , vol.12 , pp. 1-57
    • Melnikov, V.K.1
  • 12
    • 0019713774 scopus 로고
    • Bifurcation analysis near a double eigenvalue of a model chemical reaction
    • D. SCHAEFFER AND M. GOLUBITSKY, Bifurcation analysis near a double eigenvalue of a model chemical reaction, Arch. Rational Mech. Anal., 75 (1980), pp. 315-347.
    • (1980) Arch. Rational Mech. Anal. , vol.75 , pp. 315-347
    • Schaeffer, D.1    Golubitsky, M.2
  • 13
    • 84966229350 scopus 로고
    • Riemann problems for nonstrictly hyperbolic 2 × 2 systems of conservation laws
    • D. SCHAEFFER AND M. SHEARER, Riemann problems for nonstrictly hyperbolic 2 × 2 systems of conservation laws, Trans. Amer. Math. Soc., 304 (1987), pp. 267-306.
    • (1987) Trans. Amer. Math. Soc. , vol.304 , pp. 267-306
    • Schaeffer, D.1    Shearer, M.2
  • 14
    • 0001449766 scopus 로고
    • The saddle-node separatrix-loop bifurcation
    • S. SCHECTER, The saddle-node separatrix-loop bifurcation, SIAM J. Math. Anal., 18 (1987), pp. 1142-1156.
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1142-1156
    • Schecter, S.1
  • 15
    • 0002734682 scopus 로고
    • Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the melnikov integral
    • S. SCHECTER, Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the melnikov integral, Nonlinearity, 3 (1990), pp. 79-99.
    • (1990) Nonlinearity , vol.3 , pp. 79-99
    • Schecter, S.1
  • 16
    • 0001500263 scopus 로고
    • Undercompressive shocks for nonstrictly hyperbolic conservation laws
    • S. SCHECTER AND M. SHEARER, Undercompressive shocks for nonstrictly hyperbolic conservation laws, J. Dynamics Differential Equations, 3 (1991), pp. 199-271.
    • (1991) J. Dynamics Differential Equations , vol.3 , pp. 199-271
    • Schecter, S.1    Shearer, M.2
  • 17
    • 38249025011 scopus 로고
    • The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearities
    • M. SPHEARER, The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearities, J. Differential Equations, 80 (1989), pp. 343-363.
    • (1989) J. Differential Equations , vol.80 , pp. 343-363
    • Sphearer, M.1
  • 18
    • 0000979433 scopus 로고
    • Solution of the Riemann problem for a prototype 2 × 2 system of non-strictly hyperbolic conservation laws
    • M. SHEARER, D. SCHAEFFER, D. MARCHESIN, AND P. PAES-LEME, Solution of the Riemann problem for a prototype 2 × 2 system of non-strictly hyperbolic conservation laws, Arch. Rational Mech. Anal., 97 (1987), pp. 299-320.
    • (1987) Arch. Rational Mech. Anal. , vol.97 , pp. 299-320
    • Shearer, M.1    Schaeffer, D.2    Marchesin, D.3    Paes-Leme, P.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.