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Volumn 50, Issue SUPPL., 2001, Pages 109-157

Critical thresholds in Euler-Poisson equations

Author keywords

Breakdown; Critical threshold; Euler Poisson equations; Global existence; Isotropic flow

Indexed keywords


EID: 0013184506     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2001.50.2177     Document Type: Article
Times cited : (156)

References (27)
  • 1
    • 0000465767 scopus 로고
    • A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model
    • U.M. ASCHER, PETER A. MARKOWICH, P. PIETRA & C. SCHMEISER, A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model, Math. Models Methods Appl. Sci. 1 (1991), 347-376.
    • (1991) Math. Models Methods Appl. Sci. , vol.1 , pp. 347-376
    • Ascher, U.M.1    Markowich, P.A.2    Pietra, P.3    Schmeiser, C.4
  • 2
    • 21844500850 scopus 로고
    • The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models
    • U. BRAUER, A. RENDAL & O. REULA, The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models, Class. Quantum Grav. 11 (1994), 2283-2296.
    • (1994) Class. Quantum Grav. , vol.11 , pp. 2283-2296
    • Brauer, U.1    Rendal, A.2    Reula, O.3
  • 5
    • 0030210099 scopus 로고    scopus 로고
    • Convergence of shock capturing scheme for the compressible Euler-Poisson equations
    • G.-Q. CHEN & D. WANG, Convergence of shock capturing scheme for the compressible Euler-Poisson equations, Comm. Math. Phys. 179 (1996), 333-364.
    • (1996) Comm. Math. Phys. , vol.179 , pp. 333-364
    • Chen, G.-Q.1    Wang, D.2
  • 6
    • 0035627834 scopus 로고    scopus 로고
    • Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics
    • J. DOLBEAULT & G. REIN, Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics, Mathematical Models and methods in Applied Sciences 11 (2001), 407-432.
    • (2001) Mathematical Models and Methods in Applied Sciences , vol.11 , pp. 407-432
    • Dolbeault, J.1    Rein, G.2
  • 7
    • 0038250953 scopus 로고    scopus 로고
    • Formation of singularities in the Euler-Poisson equations
    • S. ENGELBERG, Formation of singularities in the Euler-Poisson equations, Physica D 98 (1996), 67-74.
    • (1996) Physica D , vol.98 , pp. 67-74
    • Engelberg, S.1
  • 8
    • 0001094592 scopus 로고
    • Solution régulière à temps petit pour l'équation d'Euler-Poisson
    • P. GAMBLIN, Solution régulière à temps petit pour l'équation d'Euler-Poisson, Comm. Partial Differential Equations 18 (1993), 731-745.
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 731-745
    • Gamblin, P.1
  • 14
    • 0034274265 scopus 로고    scopus 로고
    • Relaxation of the isothermal Euler-Poisson system to the drifi-diffusion equations
    • S. JUNCA & M. RASCLE, Relaxation of the isothermal Euler-Poisson system to the drifi-diffusion equations, Quart. Appl. Math. 58 (2000), 511-521.
    • (2000) Quart. Appl. Math. , vol.58 , pp. 511-521
    • Junca, S.1    Rascle, M.2
  • 15
    • 0000067332 scopus 로고    scopus 로고
    • Large time behavior of the solutions to a hydrodynamic model for semiconductors
    • T. LUO, R. NATALINI & Z. XIN, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math. 59 (1999), 810-830.
    • (1999) SIAM J Appl Math , vol.59 , pp. 810-830
    • Luo, T.1    Natalini, R.2    Xin, Z.3
  • 16
    • 77957028939 scopus 로고
    • On a local existence theorem for the evolution of gaseous stars
    • T. Nishida, M. Mimura & H. Fujii, eds., North-Holland/Kinokuniya
    • T. MAKINO, On a local existence theorem for the evolution of gaseous stars, In: Patterns and Waves (T. Nishida, M. Mimura & H. Fujii, eds.), North-Holland/Kinokuniya, 1986, pp. 459-479.
    • (1986) Patterns and Waves , pp. 459-479
    • Makino, T.1
  • 17
    • 84988168701 scopus 로고
    • A non-isentropic Euler-Poisson model for a collisionless plasma
    • P.A. MARKOWICH, A non-isentropic Euler-Poisson Model for a Collisionless Plasma, Math. Methods Appl. Sci. 16 (1993), 409-442.
    • (1993) Math. Methods Appl. Sci. , vol.16 , pp. 409-442
    • Markowich, P.A.1
  • 18
    • 0001257150 scopus 로고
    • Sur les solutions à symétrie sphérique de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses
    • T. MAKINO & B. PERTHAME, Sur les solutions à symétrie sphérique de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses, Japan J. Appl. math. 7 (1990), 165-170.
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 165-170
    • Makino, T.1    Perthame, B.2
  • 19
    • 21844490167 scopus 로고
    • Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation
    • P. MARCATI & R. NATALINI, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Rat. Mech. Anal. 129 (1995), 129-145.
    • (1995) Arch. Rat. Mech. Anal. , vol.129 , pp. 129-145
    • Marcati, P.1    Natalini, R.2
  • 21
    • 0000653982 scopus 로고
    • Sur l'éxistence des solutions locales de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses
    • T. MAKINO & S. UKAI, Sur l'éxistence des solutions locales de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses, J. Math. Kyoto Univ. 27 (1987), 387-399.
    • (1987) J. Math. Kyoto Univ. , vol.27 , pp. 387-399
    • Makino, T.1    Ukai, S.2
  • 22
    • 0007286985 scopus 로고
    • Nonexistence of global solutions to the Euler-Poisson equations for repulsive forces
    • B. PERTHAME, Nonexistence of global solutions to the Euler-Poisson equations for repulsive forces, Japan J. Appl. Math. 7 (1990), 363-367.
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 363-367
    • Perthame, B.1
  • 23
    • 0040646607 scopus 로고
    • Evolution and breaking of ion-acoustic waves
    • P. ROSENAU, Evolution and breaking of ion-acoustic waves, Phys. Fluids 31 (1988), 1317-1319.
    • (1988) Phys. Fluids , vol.31 , pp. 1317-1319
    • Rosenau, P.1
  • 24
    • 84875084810 scopus 로고    scopus 로고
    • Global solutions and relaxation limits of Euler-Poisson equations
    • to appear
    • D. WANG, Global solutions and relaxation limits of Euler-Poisson equations, Z. Angew. Math. Phys., to appear.
    • Z. Angew. Math. Phys.
    • Wang, D.1
  • 25
    • 84875109089 scopus 로고    scopus 로고
    • Global solutions to the equations of viscous gas flows
    • Edinburgh: Section A, to appear
    • _, Global solutions to the equations of viscous gas flows, Pro. Royal Soc. Edinburgh: Section A, to appear.
    • Pro. Royal Soc.
  • 26
    • 0031511475 scopus 로고    scopus 로고
    • Global solutions to the Euler-Poisson equations of two-carrier types in one-dimension
    • _, Global solutions to the Euler-Poisson equations of two-carrier types in one-dimension, Z. Angew. Math. Phys. 48 (1997), 680-693.
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 680-693
  • 27
    • 0002499554 scopus 로고    scopus 로고
    • Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation
    • D. WANG & G.-Q. CHEN, Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation, J. Diff. Eqs. 144 (1998), 44-65.
    • (1998) J. Diff. Eqs. , vol.144 , pp. 44-65
    • Wang, D.1    Chen, G.-Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.